Daily Papers

Generative models have the potential to transform the way we emulate Earth's changing climate. Previous generative approaches rely on weather-scale autoregression for climate emulation, but this is inherently slow for long climate horizons and has yet to demonstrate stable rollouts under nonstationary forcings. Here, we introduce Spatiotemporal Pyramid Flows (SPF), a new class of flow matching approaches that model data hierarchically across spatial and temporal scales. Inspired by cascaded video models, SPF partitions the generative trajectory into a spatiotemporal pyramid, progressively increasing spatial resolution to reduce computation and coupling each stage with an associated timescale to enable direct sampling at any temporal level in the pyramid. This design, together with conditioning each stage on prescribed physical forcings (e.g., greenhouse gases or aerosols), enables efficient, parallel climate emulation at multiple timescales. On ClimateBench, SPF outperforms strong flow matching baselines and pre-trained models at yearly and monthly timescales while offering fast sampling, especially at coarser temporal levels. To scale SPF, we curate ClimateSuite, the largest collection of Earth system simulations to date, comprising over 33,000 simulation-years across ten climate models and the first dataset to include simulations of climate interventions. We find that the scaled SPF model demonstrates good generalization to held-out scenarios across climate models. Together, SPF and ClimateSuite provide a foundation for accurate, efficient, probabilistic climate emulation across temporal scales and realistic future scenarios. Data and code is publicly available at https://github.com/stanfordmlgroup/spf .

Recent advances in video generation models have sparked interest in world models capable of simulating realistic environments. While navigation has been well-explored, physically meaningful interactions that mimic real-world forces remain largely understudied. In this work, we investigate using physical forces as a control signal for video generation and propose force prompts which enable users to interact with images through both localized point forces, such as poking a plant, and global wind force fields, such as wind blowing on fabric. We demonstrate that these force prompts can enable videos to respond realistically to physical control signals by leveraging the visual and motion prior in the original pretrained model, without using any 3D asset or physics simulator at inference. The primary challenge of force prompting is the difficulty in obtaining high quality paired force-video training data, both in the real world due to the difficulty of obtaining force signals, and in synthetic data due to limitations in the visual quality and domain diversity of physics simulators. Our key finding is that video generation models can generalize remarkably well when adapted to follow physical force conditioning from videos synthesized by Blender, even with limited demonstrations of few objects. Our method can generate videos which simulate forces across diverse geometries, settings, and materials. We also try to understand the source of this generalization and perform ablations that reveal two key elements: visual diversity and the use of specific text keywords during training. Our approach is trained on only around 15k training examples for a single day on four A100 GPUs, and outperforms existing methods on force adherence and physics realism, bringing world models closer to real-world physics interactions. We release all datasets, code, weights, and interactive video demos at our project page.

How momentum, energy, and magnetic fields are transported in the presence of macroscopic gradients is a fundamental question in plasma physics. Answering this question is especially challenging for weakly collisional, magnetized plasmas, where macroscopic gradients influence the plasma's microphysical structure. In this paper, we introduce thermodynamic forcing, a new method for systematically modeling how macroscopic gradients in magnetized or unmagnetized plasmas shape the distribution functions of constituent particles. In this method, we propose to apply an anomalous force to those particles inducing the anisotropy that would naturally emerge due to macroscopic gradients in weakly collisional plasmas. We implement thermodynamic forcing in particle-in-cell (TF-PIC) simulations using a modified Vay particle pusher and validate it against analytic solutions of the equations of motion. We then carry out a series of simulations of electron-proton plasmas with periodic boundary conditions using TF-PIC. First, we confirm that the properties of two electron-scale kinetic instabilities -- one driven by a temperature gradient and the other by pressure anisotropy -- are consistent with previous results. Then, we demonstrate that in the presence of multiple macroscopic gradients, the saturated state can differ significantly from current expectations. This work enables, for the first time, systematic and self-consistent transport modeling in weakly collisional plasmas, with broad applications in astrophysics, laser-plasma physics, and inertial confinement fusion.

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

Physical principles are fundamental to realistic visual simulation, but remain a significant oversight in transformer-based video generation. This gap highlights a critical limitation in rendering rigid body motion, a core tenet of classical mechanics. While computer graphics and physics-based simulators can easily model such collisions using Newton formulas, modern pretrain-finetune paradigms discard the concept of object rigidity during pixel-level global denoising. Even perfectly correct mathematical constraints are treated as suboptimal solutions (i.e., conditions) during model optimization in post-training, fundamentally limiting the physical realism of generated videos. Motivated by these considerations, we introduce, for the first time, a physics-aware reinforcement learning paradigm for video generation models that enforces physical collision rules directly in high-dimensional spaces, ensuring the physics knowledge is strictly applied rather than treated as conditions. Subsequently, we extend this paradigm to a unified framework, termed Mimicry-Discovery Cycle (MDcycle), which allows substantial fine-tuning while fully preserving the model's ability to leverage physics-grounded feedback. To validate our approach, we construct new benchmark PhysRVGBench and perform extensive qualitative and quantitative experiments to thoroughly assess its effectiveness.

Traditional foundation models are pre-trained on broad datasets to reduce the training resources (e.g., time, energy, labeled samples) needed for fine-tuning a wide range of downstream tasks. However, traditional foundation models struggle with out-of-distribution prediction and can produce outputs that are unrealistic and physically infeasible. We propose the notation of physics-guided foundation models (PGFM), that is, foundation models integrated with broad or general domain (e.g., scientific) physical knowledge applicable to a wide range of downstream tasks.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

The image-to-image translation abilities of generative learning models have recently made significant progress in the estimation of complex (steered) mappings between image distributions. While appearance based tasks like image in-painting or style transfer have been studied at length, we propose to investigate the potential of generative models in the context of physical simulations. Providing a dataset of 300k image-pairs and baseline evaluations for three different physical simulation tasks, we propose a benchmark to investigate the following research questions: i) are generative models able to learn complex physical relations from input-output image pairs? ii) what speedups can be achieved by replacing differential equation based simulations? While baseline evaluations of different current models show the potential for high speedups (ii), these results also show strong limitations toward the physical correctness (i). This underlines the need for new methods to enforce physical correctness. Data, baseline models and evaluation code http://www.physics-gen.org.

We verify a recent prediction (Eq. 3.50 in G. L. Eyink, Phys. Rev. X 11, 031054 (2021)) for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from [1] and compare its prediction to the measured drag force. We find excellent agreement, and, most remarkably find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements on the experimental techniques for evaluating the Josephson-Anderson relation.

We introduce StreamForce, a streaming video generation framework that enables physically grounded control through continuous force inputs. Unlike prior video models that train separate models for different force types, assume fixed forces, or rely on non-causal processing, StreamForce is a causal and unified model that responds instantly and coherently to both local and global, time-varying forces. To achieve this, we design a unified force representation as a control signal and develop a distillation pipeline for force-controllable video generation. Our model combines autoregressive efficiency with force responsiveness, sustaining stable photometric and dynamic realism. StreamForce runs at up to 16.6 FPS on a single GPU, achieving state-of-the-art performance in both force adherence and motion realism. Project website: https://neu-vi.github.io/StreamForce/

Using solar-cycle long helioseismic measurements of meridional and zonal flows in the near-surface shear layer (NSSL) of the Sun, we study their spatio-temporal variations and connections to active regions. We find that near-surface inflows towards active latitudes are part of a local circulation with an outflow away from them at depths around 0.97 R, which is also the location where the deviations in the radial gradient of rotation change sign. These results, together with opposite-signed changes over latitude and depth in the above quantities observed during the solar minimum period, point to the action of the Coriolis force on large-scale flows as the primary cause of changes in the rotation gradient within the NSSL. We also find that such Coriolis force-mediated changes in near-surface flows towards active latitudes only marginally change the amplitude of zonal flow and hence are not likely to be its driving force. Our measurements typically achieve a high signal-to-noise ratio (>5σ) for near-surface flows but can drop to 3σ near the base (0.95 R) of the NSSL. Close agreements between the depth profiles of changes in rotation gradient and in meridional flows measured from quite different global and local helioseismic techniques, respectively, show that the results are not dependent on the analysis techniques.

The Casimir effect and superconductivity are foundational quantum phenomena whose interaction remains an open question in physics. How Casimir forces behave across a superconducting transition remains unresolved, owing to the experimental difficulty of achieving alignment, cryogenic environments, and isolating small changes from competing effects. This question carries implications for electron physics, quantum gravity, and high-temperature superconductivity. Here we demonstrate an on-chip superconducting platform that overcomes these challenges, achieving one of the most parallel Casimir configurations to date. Our microchip-based cavities achieve unprecedented area-to-separation ratio between plates, exceeding previous Casimir experiments by orders of magnitude and generating the strongest Casimir forces yet between compliant surfaces. Scanning tunneling microscopy (STM) is used for the first time to directly detect the resonant motion of a suspended membrane, with subatomic precision in both lateral positioning and displacement. Such precision measurements across a superconducting transition allow for the suppression of all van der Waals, electrostatic, and thermal effects. Preliminary measurements suggest superconductivity-dependent shifts in the Casimir force, motivating further investigation and comparison with theories. By uniting extreme parallelism, nanomechanics, and STM readout, our platform opens a new experimental frontier at the intersection of Casimir physics and superconductivity.

The ultimate goal of video generation is to satisfy a fundamental trilemma: achieving high visual quality, maintaining rigorous physical consistency, and enabling precise controllability. While recent models can maintain this balance in simple, isolated scenarios, we observe that this equilibrium is fragile and often breaks down as scene complexity increases (e.g., involving collisions or dense traffic). To address this, we introduce Motion Forcing, a framework designed to stabilize this trilemma even in complex generative tasks. Our key insight is to explicitly decouple physical reasoning from visual synthesis via a hierarchical ``Point-Shape-Appearance'' paradigm. This approach decomposes generation into verifiable stages: modeling complex dynamics as sparse geometric anchors (Point), expanding them into dynamic depth maps that explicitly resolve 3D geometry (Shape), and finally rendering high-fidelity textures (Appearance). Furthermore, to foster robust physical understanding, we employ a Masked Point Recovery strategy. By randomly masking input anchors during training and enforcing the reconstruction of complete dynamic depth, the model is compelled to move beyond passive pattern matching and learn latent physical laws (e.g., inertia) to infer missing trajectories. Extensive experiments on autonomous driving benchmarks show that Motion Forcing significantly outperforms state-of-the-art baselines, maintaining trilemma stability across complex scenes. Evaluations on physics and robotics further confirm our framework's generality.

This manuscript presents an historical perspective prepared by Barry Ninham and Colin Pask in 1969 on the connection between quantum electrodynamics theory and nucleon interactions. A new theory of strong interactions based on electromagnetic considerations is proposed. Energy and force range magnitudes are correctly given. A new theory of the pion emerges and the pion mass and lifetime are calculated. No strong interaction coupling constant is required.

Video generation models have achieved remarkable progress in creating high-quality, photorealistic content. However, their ability to accurately simulate physical phenomena remains a critical and unresolved challenge. This paper presents PhyWorldBench, a comprehensive benchmark designed to evaluate video generation models based on their adherence to the laws of physics. The benchmark covers multiple levels of physical phenomena, ranging from fundamental principles like object motion and energy conservation to more complex scenarios involving rigid body interactions and human or animal motion. Additionally, we introduce a novel ""Anti-Physics"" category, where prompts intentionally violate real-world physics, enabling the assessment of whether models can follow such instructions while maintaining logical consistency. Besides large-scale human evaluation, we also design a simple yet effective method that could utilize current MLLM to evaluate the physics realism in a zero-shot fashion. We evaluate 12 state-of-the-art text-to-video generation models, including five open-source and five proprietary models, with a detailed comparison and analysis. we identify pivotal challenges models face in adhering to real-world physics. Through systematic testing of their outputs across 1,050 curated prompts-spanning fundamental, composite, and anti-physics scenarios-we identify pivotal challenges these models face in adhering to real-world physics. We then rigorously examine their performance on diverse physical phenomena with varying prompt types, deriving targeted recommendations for crafting prompts that enhance fidelity to physical principles.

Recent advancements in video generation have witnessed significant progress, especially with the rapid advancement of diffusion models. Despite this, their deficiencies in physical cognition have gradually received widespread attention - generated content often violates the fundamental laws of physics, falling into the dilemma of ''visual realism but physical absurdity". Researchers began to increasingly recognize the importance of physical fidelity in video generation and attempted to integrate heuristic physical cognition such as motion representations and physical knowledge into generative systems to simulate real-world dynamic scenarios. Considering the lack of a systematic overview in this field, this survey aims to provide a comprehensive summary of architecture designs and their applications to fill this gap. Specifically, we discuss and organize the evolutionary process of physical cognition in video generation from a cognitive science perspective, while proposing a three-tier taxonomy: 1) basic schema perception for generation, 2) passive cognition of physical knowledge for generation, and 3) active cognition for world simulation, encompassing state-of-the-art methods, classical paradigms, and benchmarks. Subsequently, we emphasize the inherent key challenges in this domain and delineate potential pathways for future research, contributing to advancing the frontiers of discussion in both academia and industry. Through structured review and interdisciplinary analysis, this survey aims to provide directional guidance for developing interpretable, controllable, and physically consistent video generation paradigms, thereby propelling generative models from the stage of ''visual mimicry'' towards a new phase of ''human-like physical comprehension''.

Recent advancements in video generation have enabled the development of ``world models'' capable of simulating potential futures for robotics and planning. However, specifying precise goals for these models remains a challenge; text instructions are often too abstract to capture physical nuances, while target images are frequently infeasible to specify for dynamic tasks. To address this, we introduce Goal Force, a novel framework that allows users to define goals via explicit force vectors and intermediate dynamics, mirroring how humans conceptualize physical tasks. We train a video generation model on a curated dataset of synthetic causal primitives-such as elastic collisions and falling dominos-teaching it to propagate forces through time and space. Despite being trained on simple physics data, our model exhibits remarkable zero-shot generalization to complex, real-world scenarios, including tool manipulation and multi-object causal chains. Our results suggest that by grounding video generation in fundamental physical interactions, models can emerge as implicit neural physics simulators, enabling precise, physics-aware planning without reliance on external engines. We release all datasets, code, model weights, and interactive video demos at our project page.

The basic framework of the superfluid vortex model for pulsar glitches, though, is well accepted; there is a lack of consensus on the possible trigger mechanism responsible for the simultaneous release of a large number (sim 10^{17}) of superfluid vortices from the inner crust. Here, we propose a simple trigger mechanism to explain such catastrophic events of vortex unpinning. We treat a superfluid vortex line as a classical massive straight string with well-defined string tension stretching along the rotation axis of pulsars. The crustquake-induced lattice vibration of the inner crust can act as a driving force for the transverse oscillation of the string. Such forced oscillation near resonance causes the bending of the vortex lines, disturbing their equilibrium configuration and resulting in the unpinning of vortices. We consider unpinning from the inner crust's so-called {\it strong (nuclear)} pinning region, where the vortices are likely pinned to the nuclear sites. We also comment on vortex unpinning from the interstitial pinning region of the inner crust. We sense that unifying crustquake with the superfluid vortex model can naturally explain the cause of large-scale vortex unpinning and generation of large-size pulsar glitches.

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We are living in an era of rapid transformation. These methods have the potential to redefine what's possible in computational science.

We present PhysInOne, a large-scale synthetic dataset addressing the critical scarcity of physically-grounded training data for AI systems. Unlike existing datasets limited to merely hundreds or thousands of examples, PhysInOne provides 2 million videos across 153,810 dynamic 3D scenes, covering 71 basic physical phenomena in mechanics, optics, fluid dynamics, and magnetism. Distinct from previous works, our scenes feature multiobject interactions against complex backgrounds, with comprehensive ground-truth annotations including 3D geometry, semantics, dynamic motion, physical properties, and text descriptions. We demonstrate PhysInOne's efficacy across four emerging applications: physics-aware video generation, long-/short-term future frame prediction, physical property estimation, and motion transfer. Experiments show that fine-tuning foundation models on PhysInOne significantly enhances physical plausibility, while also exposing critical gaps in modeling complex physical dynamics and estimating intrinsic properties. As the largest dataset of its kind, orders of magnitude beyond prior works, PhysInOne establishes a new benchmark for advancing physics-grounded world models in generation, simulation, and embodied AI.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

We present an update to ECMWF's machine-learned weather forecasting model AIFS Single with several key improvements. The model now incorporates physical consistency constraints through bounding layers, an updated training schedule, and an expanded set of variables. The physical constraints substantially improve precipitation forecasts and the new variables show a high level of skill. Upper-air headline scores also show improvement over the previous AIFS version. The AIFS has been fully operational at ECMWF since the 25th of February 2025.

We investigate how to enhance the physical fidelity of video generation models by leveraging synthetic videos derived from computer graphics pipelines. These rendered videos respect real-world physics, such as maintaining 3D consistency, and serve as a valuable resource that can potentially improve video generation models. To harness this potential, we propose a solution that curates and integrates synthetic data while introducing a method to transfer its physical realism to the model, significantly reducing unwanted artifacts. Through experiments on three representative tasks emphasizing physical consistency, we demonstrate its efficacy in enhancing physical fidelity. While our model still lacks a deep understanding of physics, our work offers one of the first empirical demonstrations that synthetic video enhances physical fidelity in video synthesis. Website: https://kevinz8866.github.io/simulation/

The classical Coulomb gas model has served as one of the most versatile frameworks in statistical physics, connecting a vast range of phenomena across many different areas. Nonequilibrium generalisations of this model have so far been studied much more scarcely. With the abundance of contemporary research into active and driven systems, one would naturally expect that such generalisations of systems with long-ranged Coulomb-like interactions will form a fertile playground for interesting developments. Here, we present two examples of novel macroscopic behaviour that arise from nonequilibrium fluctuations in long-range interacting systems, namely (1) unscreened long-ranged correlations in strong electrolytes driven by an external electric field and the associated fluctuation-induced forces in the confined Casimir geometry, and (2) out-of-equilibrium critical behaviour in self-chemotactic models that incorporate the particle polarity in the chemotactic response of the cells. Both of these systems have nonlocal Coulomb-like interactions among their constituent particles, namely, the electrostatic interactions in the case of the driven electrolyte, and the chemotactic forces mediated by fast-diffusing signals in the case of self-chemotactic systems. The results presented here hint to the rich phenomenology of nonequilibrium effects that can arise from strong fluctuations in Coulomb interacting systems, and a rich variety of potential future directions, which are discussed.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

Generative video models achieve high visual fidelity but often violate basic physical principles, limiting reliability in real-world settings. Prior attempts to inject physics rely on conditioning: frame-level signals are domain-specific and short-horizon, while global text prompts are coarse and noisy, missing fine-grained dynamics. We present PhysVid, a physics-aware local conditioning scheme that operates over temporally contiguous chunks of frames. Each chunk is annotated with physics-grounded descriptions of states, interactions, and constraints, which are fused with the global prompt via chunk-aware cross-attention during training. At inference, we introduce negative physics prompts (descriptions of locally relevant law violations) to steer generation away from implausible trajectories. On VideoPhy, PhysVid improves physical commonsense scores by approx 33% over baseline video generators, and by up to approx 8% on VideoPhy2. These results show that local, physics-aware guidance substantially increases physical plausibility in generative video and marks a step toward physics-grounded video models.

Generative Artificial Intelligence (AI) has rapidly advanced the field of computer vision by enabling machines to create and interpret visual data with unprecedented sophistication. This transformation builds upon a foundation of generative models to produce realistic images, videos, and 3D/4D content. Conventional generative models primarily focus on visual fidelity while often neglecting the physical plausibility of the generated content. This gap limits their effectiveness in applications that require adherence to real-world physical laws, such as robotics, autonomous systems, and scientific simulations. As generative models evolve to increasingly integrate physical realism and dynamic simulation, their potential to function as "world simulators" expands. Therefore, the field of physics-aware generation in computer vision is rapidly growing, calling for a comprehensive survey to provide a structured analysis of current efforts. To serve this purpose, the survey presents a systematic review, categorizing methods based on how they incorporate physical knowledge, either through explicit simulation or implicit learning. It also analyzes key paradigms, discusses evaluation protocols, and identifies future research directions. By offering a comprehensive overview, this survey aims to help future developments in physically grounded generation for computer vision. The reviewed papers are summarized at https://tinyurl.com/Physics-Aware-Generation.

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.

Image editing has achieved remarkable progress recently. Modern editing models could already follow complex instructions to manipulate the original content. However, beyond completing the editing instructions, the accompanying physical effects are the key to the generation realism. For example, removing an object should also remove its shadow, reflections, and interactions with nearby objects. Unfortunately, existing models and benchmarks mainly focus on instruction completion but overlook these physical effects. So, at this moment, how far are we from physically realistic image editing? To answer this, we introduce PICABench, which systematically evaluates physical realism across eight sub-dimension (spanning optics, mechanics, and state transitions) for most of the common editing operations (add, remove, attribute change, etc). We further propose the PICAEval, a reliable evaluation protocol that uses VLM-as-a-judge with per-case, region-level human annotations and questions. Beyond benchmarking, we also explore effective solutions by learning physics from videos and construct a training dataset PICA-100K. After evaluating most of the mainstream models, we observe that physical realism remains a challenging problem with large rooms to explore. We hope that our benchmark and proposed solutions can serve as a foundation for future work moving from naive content editing toward physically consistent realism.

Video generation models are increasingly used as world simulators for storytelling, simulation, and embodied AI. As these models advance, a key question arises: do generated videos obey the physical laws of the real world? Existing evaluations largely rely on automated metrics or coarse human judgments such as preferences or rubric-based checks. While useful for assessing perceptual quality, these methods provide limited insight into when and why generated dynamics violate real-world physical constraints. We introduce Physion-Eval, a large-scale benchmark of expert human reasoning for diagnosing physical realism failures in videos generated by five state-of-the-art models across egocentric and exocentric views, containing 10,990 expert reasoning traces spanning 22 fine-grained physical categories. Each generated video is derived from a corresponding real-world reference video depicting a clear physical process, and annotated with temporally localized glitches, structured failure categories, and natural-language explanations of the violated physical behavior. Using this dataset, we reveal a striking limitation of current video generation models: in physics-critical scenarios, 83.3% of exocentric and 93.5% of egocentric generated videos exhibit at least one human-identifiable physical glitch. We hope Physion-Eval will set a new standard for physical realism evaluation and guide the development of physics-grounded video generation. The benchmark is publicly available at https://huggingface.co/datasets/PhysionLabs/Physion-Eval.

Recent advances in video generation have shown remarkable potential for constructing world simulators. However, current models still struggle to produce physically consistent results, particularly when handling large-scale or complex dynamics. This limitation arises primarily because existing approaches respond isotropically to physical prompts and neglect the fine-grained alignment between generated content and localized physical cues. To address these challenges, we propose ProPhy, a Progressive Physical Alignment Framework that enables explicit physics-aware conditioning and anisotropic generation. ProPhy employs a two-stage Mixture-of-Physics-Experts (MoPE) mechanism for discriminative physical prior extraction, where Semantic Experts infer semantic-level physical principles from textual descriptions, and Refinement Experts capture token-level physical dynamics. This mechanism allows the model to learn fine-grained, physics-aware video representations that better reflect underlying physical laws. Furthermore, we introduce a physical alignment strategy that transfers the physical reasoning capabilities of vision-language models (VLMs) into the Refinement Experts, facilitating a more accurate representation of dynamic physical phenomena. Extensive experiments on physics-aware video generation benchmarks demonstrate that ProPhy produces more realistic, dynamic, and physically coherent results than existing state-of-the-art methods.

Video generation models internalize physical realism as their prior. Anime deliberately violates physics: smears, impact frames, chibi shifts; and its thousands of coexisting artistic conventions yield no single "physics of anime" a model can absorb. Physics-biased models therefore flatten the artistry that defines the medium or collapse under its stylistic variance. We present AniMatrix, a video generation model that targets artistic rather than physical correctness through a dual-channel conditioning mechanism and a three-step transition: redefine correctness, override the physics prior, and distinguish art from failure. First, a Production Knowledge System encodes anime as a structured taxonomy of controllable production variables (Style, Motion, Camera, VFX), and AniCaption infers these variables from pixels as directorial directives. A trainable tag encoder preserves the field-value structure of this taxonomy while a frozen T5 encoder handles free-form narrative; dual-path injection (cross-attention for fine-grained control, AdaLN modulation for global enforcement) ensures categorical directives are never diluted by open-ended text. Second, a style-motion-deformation curriculum transitions the model from near-physical motion to full anime expressiveness. Third, deformation-aware preference optimization with a domain-specific reward model separates intentional artistry from pathological collapse. On an anime-specific human evaluation with five production dimensions scored by professional animators, AniMatrix ranks first on four of five, with the largest gains over Seedance-Pro 1.0 on Prompt Understanding (+0.70, +22.4 percent) and Artistic Motion (+0.55, +16.9 percent). We are preparing accompanying resources for public release to support reproducibility and follow-up research.

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from being fully explored in the field of physics-informed machine learning. We believe that the interdisciplinary research of physics-informed machine learning will significantly propel research progress, foster the creation of more effective machine learning models, and also offer invaluable assistance in addressing long-standing problems in related disciplines.

Machine Learning Force Fields (MLFFs) are a promising alternative to expensive ab initio quantum mechanical molecular simulations. Given the diversity of chemical spaces that are of interest and the cost of generating new data, it is important to understand how MLFFs generalize beyond their training distributions. In order to characterize and better understand distribution shifts in MLFFs, we conduct diagnostic experiments on chemical datasets, revealing common shifts that pose significant challenges, even for large foundation models trained on extensive data. Based on these observations, we hypothesize that current supervised training methods inadequately regularize MLFFs, resulting in overfitting and learning poor representations of out-of-distribution systems. We then propose two new methods as initial steps for mitigating distribution shifts for MLFFs. Our methods focus on test-time refinement strategies that incur minimal computational cost and do not use expensive ab initio reference labels. The first strategy, based on spectral graph theory, modifies the edges of test graphs to align with graph structures seen during training. Our second strategy improves representations for out-of-distribution systems at test-time by taking gradient steps using an auxiliary objective, such as a cheap physical prior. Our test-time refinement strategies significantly reduce errors on out-of-distribution systems, suggesting that MLFFs are capable of and can move towards modeling diverse chemical spaces, but are not being effectively trained to do so. Our experiments establish clear benchmarks for evaluating the generalization capabilities of the next generation of MLFFs. Our code is available at https://tkreiman.github.io/projects/mlff_distribution_shifts/.

Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining. Access to a Physics Foundation Model (PFM) would be transformative -- democratizing access to high-fidelity simulations, accelerating scientific discovery, and eliminating the need for specialized solver development. Yet current physics-aware machine learning approaches remain fundamentally limited to single, narrow domains and require retraining for each new system. We present the General Physics Transformer (GPhyT), trained on 1.8 TB of diverse simulation data, that demonstrates foundation model capabilities are achievable for physics. Our key insight is that transformers can learn to infer governing dynamics from context, enabling a single model to simulate fluid-solid interactions, shock waves, thermal convection, and multi-phase dynamics without being told the underlying equations. GPhyT achieves three critical breakthroughs: (1) superior performance across multiple physics domains, outperforming specialized architectures by up to 29x, (2) zero-shot generalization to entirely unseen physical systems through in-context learning, and (3) stable long-term predictions through 50-timestep rollouts. By establishing that a single model can learn generalizable physical principles from data alone, this work opens the path toward a universal PFM that could transform computational science and engineering.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

Physical simulations produce excellent predictions of weather effects. Neural radiance fields produce SOTA scene models. We describe a novel NeRF-editing procedure that can fuse physical simulations with NeRF models of scenes, producing realistic movies of physical phenomena in those scenes. Our application -- Climate NeRF -- allows people to visualize what climate change outcomes will do to them. ClimateNeRF allows us to render realistic weather effects, including smog, snow, and flood. Results can be controlled with physically meaningful variables like water level. Qualitative and quantitative studies show that our simulated results are significantly more realistic than those from SOTA 2D image editing and SOTA 3D NeRF stylization.

As LLMs advance their reasoning capabilities about the physical world, the absence of rigorous benchmarks for evaluating their ability to generate scientifically valid physical models has become a critical gap. Computational mechanics, which develops and applies mathematical models and numerical methods to predict the behavior of physical systems under forces, deformation, and constraints, provides an ideal foundation for structured scientific reasoning evaluation. Problems follow clear mathematical structure, enforce strict physical and numerical constraints, and support objective verification. The discipline requires constructing explicit models of physical systems and reasoning about geometry, spatial relationships, and material behavior, connecting directly to emerging AI goals in physical reasoning and world modeling. We introduce FEM-Bench, a computational mechanics benchmark designed to evaluate the ability of LLMs to generate correct finite element method (FEM) and related code. FEM-Bench 2025 contains a suite of introductory but nontrivial tasks aligned with material from a first graduate course on computational mechanics. These tasks capture essential numerical and physical modeling challenges while representing only a small fraction of the complexity present in the discipline. Despite their simplicity, state-of-the-art LLMs do not reliably solve all of them. In a five attempt run, the best performing model at function writing, Gemini 3 Pro, completed 30/33 tasks at least once and 26/33 tasks all five times. The best performing model at unit test writing, GPT-5, had an Average Joint Success Rate of 73.8%. Other popular models showed broad performance variation. FEM-Bench establishes a structured foundation for evaluating AI-generated scientific code, and future iterations will incorporate increasingly sophisticated tasks to track progress as models evolve.

The Sun's outer atmosphere, the corona, is maintained at mega-Kelvin temperatures and fills the heliosphere with a supersonic outflowing wind. The dissipation of magnetic waves and direct electric currents are likely to be the most significant processes for heating the corona, but a lively debate exists on their relative roles. Here, we suggest that the two are often intrinsically linked, since magnetic waves may trigger current dissipation, and impulsive reconnection can launch magnetic waves. We present a study of the first of these processes by using a 2D physics-based numerical simulation using the Adaptive Mesh Refined (AMR) Versatile Advection Code (VAC). Magnetic waves such as fast magnetoacoustic waves are often observed to propagate in the large-scale corona and interact with local magnetic structures. The present numerical simulations show how the propagation of magnetic disturbances towards a null point or separator can lead to the accumulation of the electric currents. Lorentz forces can laterally push and vertically stretch the magnetic fields, forming a current sheet with a strong magnetic-field gradient. The magnetic field lines then break and reconnect, and so contribute towards coronal heating. Numerical results are presented that support these ideas and support the concept of a symbiosis between waves and reconnection in heating the solar corona.

Recent advances in generative foundational models, often termed "world models," have propelled interest in applying them to critical tasks like robotic planning and autonomous system training. For reliable deployment, these models must exhibit high physical fidelity, accurately simulating real-world dynamics. Existing physics-based video benchmarks, however, suffer from entanglement, where a single test simultaneously evaluates multiple physical laws and concepts, fundamentally limiting their diagnostic capability. We introduce WorldBench, a novel video-based benchmark specifically designed for concept-specific, disentangled evaluation, allowing us to rigorously isolate and assess understanding of a single physical concept or law at a time. To make WorldBench comprehensive, we design benchmarks at two different levels: 1) an evaluation of intuitive physical understanding with concepts such as object permanence or scale/perspective, and 2) an evaluation of low-level physical constants and material properties such as friction coefficients or fluid viscosity. When SOTA video-based world models are evaluated on WorldBench, we find specific patterns of failure in particular physics concepts, with all tested models lacking the physical consistency required to generate reliable real-world interactions. Through its concept-specific evaluation, WorldBench offers a more nuanced and scalable framework for rigorously evaluating the physical reasoning capabilities of video generation and world models, paving the way for more robust and generalizable world-model-driven learning.

Thermophoresis is the migration of a particle due to a thermal gradient. Here, we theoretically uncover the quantum version of thermophoresis. As a proof of principle, we analytically find a thermophoretic force on a trapped quantum particle having three energy levels in Lambda configuration. We then consider a model of N sites, each coupled to its first neighbors and subjected to a local bath at a certain temperature, so as to show numerically how quantum thermophoresis behaves with increasing delocalization of the quantum particle. We discuss how negative thermophoresis and the Dufour effect appear in the quantum regime.

A longstanding goal in computer vision is to model motions from videos, while the representations behind motions, i.e. the invisible physical interactions that cause objects to deform and move, remain largely unexplored. In this paper, we study how to recover the invisible forces from visual observations, e.g., estimating the wind field by observing a leaf falling to the ground. Our key innovation is an end-to-end differentiable inverse graphics framework, which jointly models object geometry, physical properties, and interactions directly from videos. Through backpropagation, our approach enables the recovery of force representations from object motions. We validate our method on both synthetic and real-world scenarios, and the results demonstrate its ability to infer plausible force fields from videos. Furthermore, we show the potential applications of our approach, including physics-based video generation and editing. We hope our approach sheds light on understanding and modeling the physical process behind pixels, bridging the gap between vision and physics. Please check more video results in our https://chaoren2357.github.io/seeingthewind/{project page}.

The transition from symbolic manipulation to science-grade reasoning represents a pivotal frontier for Large Language Models (LLMs), with physics serving as the critical test anchor for binding abstract logic to physical reality. Physics demands that a model maintain physical consistency with the laws governing the universe, a task that fundamentally requires multimodal perception to ground abstract logic in reality. At the Olympiad level, diagrams are often constitutive rather than illustrative, containing essential constraints, such as boundary conditions and spatial symmetries, that are absent from the text. To bridge this visual-logical gap, we introduce P1-VL, a family of open-source vision-language models engineered for advanced scientific reasoning. Our method harmonizes Curriculum Reinforcement Learning, which employs progressive difficulty expansion to stabilize post-training, with Agentic Augmentation, enabling iterative self-verification at inference. Evaluated on HiPhO, a rigorous benchmark of 13 exams from 2024-2025, our flagship P1-VL-235B-A22B becomes the first open-source Vision-Language Model (VLM) to secure 12 gold medals and achieves the state-of-the-art performance in the open-source models. Our agent-augmented system achieves the No.2 overall rank globally, trailing only Gemini-3-Pro. Beyond physics, P1-VL demonstrates remarkable scientific reasoning capacity and generalizability, establishing significant leads over base models in STEM benchmarks. By open-sourcing P1-VL, we provide a foundational step toward general-purpose physical intelligence to better align visual perceptions with abstract physical laws for machine scientific discovery.

Recent rapid advancements in text-to-video (T2V) generation, such as SoRA and Kling, have shown great potential for building world simulators. However, current T2V models struggle to grasp abstract physical principles and generate videos that adhere to physical laws. This challenge arises primarily from a lack of clear guidance on physical information due to a significant gap between abstract physical principles and generation models. To this end, we introduce the World Simulator Assistant (WISA), an effective framework for decomposing and incorporating physical principles into T2V models. Specifically, WISA decomposes physical principles into textual physical descriptions, qualitative physical categories, and quantitative physical properties. To effectively embed these physical attributes into the generation process, WISA incorporates several key designs, including Mixture-of-Physical-Experts Attention (MoPA) and a Physical Classifier, enhancing the model's physics awareness. Furthermore, most existing datasets feature videos where physical phenomena are either weakly represented or entangled with multiple co-occurring processes, limiting their suitability as dedicated resources for learning explicit physical principles. We propose a novel video dataset, WISA-32K, collected based on qualitative physical categories. It consists of 32,000 videos, representing 17 physical laws across three domains of physics: dynamics, thermodynamics, and optics. Experimental results demonstrate that WISA can effectively enhance the compatibility of T2V models with real-world physical laws, achieving a considerable improvement on the VideoPhy benchmark. The visual exhibitions of WISA and WISA-32K are available in the https://360cvgroup.github.io/WISA/.

The use of chemical warfare agents (CWAs) in modern warfare cannot be disregarded due to their ease of use and potential for large-scale incapacitation. An effective countermeasure involves the physical adsorption of these agents, preventing their entry through the respiratory tract by non-specific adsorption. In this study, we investigate the physical interaction between potential adsorbents and model gases mimicking CWAs, thereby identifying sufficient conditions for higher physical adsorption performance. Our findings reveal that the physical adsorption capacity is highly sensitive to the surface properties of the adsorbents, with uniform development of micropores, rather than solely high surface area, emerging as a critical factor. Additionally, we identified the potential of porous organic polymers as promising alternatives to conventional activated carbon-based adsorbents. Through a facile introduction of polar sulfone functional groups on the polymer surface, we demonstrated that these polar surface polymers exhibit physical adsorption capabilities for formaldehyde under ambient conditions comparable to high-performance activated carbons. Notably, the superior activated carbon possessed a high BET surface area of 2400 m^2/g and an exceptionally uniform micropore structure with an average pore size of approximately 11 Angstroms. This research paves the way for designing adsorbents with high physical adsorption capacities tailored for CWAs protection, offering a significant advancement in developing next-generation protective materials.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons for their benefits, especially when used in combination. Here we treat the embeddings of images as point particles and consider model optimization as a dynamic process on this system of particles. Our dynamic model combines an attractive force for similar images, a locally dispersive force to avoid local collapse, and a global dispersive force to achieve a globally-homogeneous distribution of particles. The dynamic perspective highlights the advantage of using a delayed-parameter image embedding (a la BYOL) together with multiple views of the same image. It also uses a purely-dynamic local dispersive force (Brownian motion) that shows improved performance over other methods and does not require knowledge of other particle coordinates. The method is called MSBReg which stands for (i) a Multiview centroid loss, which applies an attractive force to pull different image view embeddings toward their centroid, (ii) a Singular value loss, which pushes the particle system toward spatially homogeneous density, (iii) a Brownian diffusive loss. We evaluate downstream classification performance of MSBReg on ImageNet as well as transfer learning tasks including fine-grained classification, multi-class object classification, object detection, and instance segmentation. In addition, we also show that applying our regularization term to other methods further improves their performance and stabilize the training by preventing a mode collapse.

Machine learning force fields (MLFFs) have revolutionized molecular simulations by providing quantum mechanical accuracy at the speed of molecular mechanical computations. However, a fundamental reliance of these models on fixed-cutoff architectures limits their applicability to macromolecular systems where long-range interactions dominate. We demonstrate that this locality constraint causes force prediction errors to scale monotonically with system size, revealing a critical architectural bottleneck. To overcome this, we establish the systematically designed MolLR25 ({Mol}ecules with {L}ong-{R}ange effect) benchmark up to 1200 atoms, generated using high-fidelity DFT, and introduce E2Former-LSR, an equivariant transformer that explicitly integrates long-range attention blocks. E2Former-LSR exhibits stable error scaling, achieves superior fidelity in capturing non-covalent decay, and maintains precision on complex protein conformations. Crucially, its efficient design provides up to 30% speedup compared to purely local models. This work validates the necessity of non-local architectures for generalizable MLFFs, enabling high-fidelity molecular dynamics for large-scale chemical and biological systems.

We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with C^{1,frac{4{3}}-1-varepsilon}cap L^{2} force that develop a singularity in finite time. Importantly, the force preserves this regularity at the blow-up time. Moreover, the forces in the vorticity and density equations have compact support. The mechanism behind the blow-up is an accumulated hysteresis effect on the vorticity caused by an infinite chain of "degenerate" pendula and flickering density.

AI video generation is undergoing a revolution, with quality and realism advancing rapidly. These advances have led to a passionate scientific debate: Do video models learn ``world models'' that discover laws of physics -- or, alternatively, are they merely sophisticated pixel predictors that achieve visual realism without understanding the physical principles of reality? We address this question by developing Physics-IQ, a comprehensive benchmark dataset that can only be solved by acquiring a deep understanding of various physical principles, like fluid dynamics, optics, solid mechanics, magnetism and thermodynamics. We find that across a range of current models (Sora, Runway, Pika, Lumiere, Stable Video Diffusion, and VideoPoet), physical understanding is severely limited, and unrelated to visual realism. At the same time, some test cases can already be successfully solved. This indicates that acquiring certain physical principles from observation alone may be possible, but significant challenges remain. While we expect rapid advances ahead, our work demonstrates that visual realism does not imply physical understanding. Our project page is at https://physics-iq.github.io; code at https://github.com/google-deepmind/physics-IQ-benchmark.

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance. To this end, we propose a novel method to selectively incorporate the physics models with the kinematics observations in an online setting, inspired by a neural Kalman-filtering approach. We develop a control loop as a meta-PD controller to predict internal joint torques and external reaction forces, followed by a physics-based motion simulation. A recurrent neural network is introduced to realize a Kalman filter that attentively balances the kinematics input and simulated motion, resulting in an optimal-state dynamics prediction. We show that this filtering step is crucial to provide an online supervision that helps balancing the shortcoming of the respective input motions, thus being important for not only capturing accurate global motion trajectories but also producing physically plausible human poses. The proposed approach excels in the physics-based human pose estimation task and demonstrates the physical plausibility of the predictive dynamics, compared to state of the art. The code is available on https://github.com/cuongle1206/OSDCap

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

The AMS-02 experiment recently published time-dependent fluxes of deuterons (D) from May 2011 to April 2021, divided into 33 periods of four Bartels rotations each. These temporal structures are associated with solar modulation. In this study, three modified force-field approximation are employed to examine the long-term behavior of cosmic-ray (CR) isotopes such as D, ^3He, and ^4He, as well as the ratios D/^3He and ^3He/^4He. The solar modulation potential is rigidity-dependent for these modified force-field approximation models. Due to the unknown local interstellar spectrum (LIS) for these isotopes, we utilize the Non-LIS method for solar modulation. By fitting to the AMS-02 time-dependent fluxes, we derive the solar modulation parameters. Our findings prove the assumption in literature that all isotopes can be fitted using the same solar modulation parameters and it shown that the modified FFA models are validated parametrization for solar modulation. Based on these, we forecast the daily fluxes of D, ^3He and ^4He from 2011 to 2020.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

Generative world models are increasingly used for video generation, where learned simulators are expected to capture the physical rules that govern real-world dynamics. However, evaluating whether generated videos actually follow these rules remains challenging. Existing physics-focused video benchmarks have made important progress, but they still face three key challenges, including the coarse evaluation frameworks that hide law-specific failures, response biases and fatigue that undermine the validity of annotation judgments, and automated evaluators that are insufficiently physics-aware or difficult to audit. To address those challenges, we introduce PhyGround, a criteria-grounded benchmark for evaluating physical reasoning in video generation. The benchmark contains 250 curated prompts, each augmented with an expected physical outcome, and a taxonomy of 13 physical laws across solid-body mechanics, fluid dynamics, and optics. Each law is operationalized through observable sub-questions to enable per-law diagnostics. We evaluate eight modern video generation models through a large-scale, quality-controlled human study, grounded on social science lab experiment design. A total of 459 annotators provided 5,796 complete annotations and over 37.4K fine-grained labels; after quality control, the retained annotations exhibited high split-half model-ranking correlations (Spearman's rho > 0.90). To support reproducible automated evaluation, we release PhyJudge-9B, an open physics-specialized VLM judge. PhyJudge-9B achieves substantially lower aggregate relative bias than Gemini-3.1-Pro (3.3% vs. 16.6%). We release prompts, human annotations, model checkpoints, and evaluation code on the project page https://phyground.github.io/.

We propose a self-consistent explanation of Rieger-type periodicities, the Schwabe cycle, and the Suess-de Vries cycle of the solar dynamo in terms of resonances of various wave phenomena with gravitational forces exerted by the orbiting planets. Starting on the high-frequency side, we show that the two-planet spring tides of Venus, Earth and Jupiter are able to excite magneto-Rossby waves which can be linked with typical Rieger-type periods. We argue then that the 11.07-year beat period of those magneto-Rossby waves synchronizes an underlying conventional alpha-Omega-dynamo, by periodically changing either the field storage capacity in the tachocline or some portion of the alpha-effect therein. We also strengthen the argument that the Suess-de Vries cycle appears as an 193-year beat period between the 22.14-year Hale cycle and a spin-orbit coupling effect related with the 19.86-year rosette-like motion of the Sun around the barycenter.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently diverse dynamics, while varying resolutions and dimensionalities challenge efficient training on modern hardware. Through empirical and theoretical analysis, we incorporate new approaches to mitigate these obstacles, including a harmonic-analysis-based stabilization method, load-balanced distributed 2D and 3D training strategies, and compute-adaptive tokenization. Using these tools, we develop Walrus, a transformer-based foundation model developed primarily for fluid-like continuum dynamics. Walrus is pretrained on nineteen diverse scenarios spanning astrophysics, geoscience, rheology, plasma physics, acoustics, and classical fluids. Experiments show that Walrus outperforms prior foundation models on both short and long term prediction horizons on downstream tasks and across the breadth of pretraining data, while ablation studies confirm the value of our contributions to forecast stability, training throughput, and transfer performance over conventional approaches. Code and weights are released for community use.

Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explosions, in which small perturbations at a density interface grow into chaotic, multiscale mixing as a lighter fluid accelerates into a heavier one. Standard ML models struggle with RTI, and despite over a century of theoretical, numerical, and experimental work, it carries an unresolved discrepancy between simulation and experiment: the late-time mixing growth rate, α, measured in most laboratory experiments (sim 0.06-0.07), is roughly three times the value from idealized direct numerical simulations (DNS, sim 0.02). The gap's origin remains debated. These properties make RTI a stringent test for a question that matters well beyond RTI: can foundation models trained only on simulations generalise to sparse, messy, and noisy laboratory settings? We finetune Walrus, a foundation model for continuum dynamics, on three or fewer DNS realizations and recover key RTI physics over long rollouts. Applied zero-shot to sliding-barrier laboratory data, the finetuned model leaves the DNS-like regime and enters the observed growth band, having never seen a single experimental sample. These results provide independent, data-driven evidence that initial conditions play a crucial role in the longstanding sim-experiment gap in α. The model also generalises zero-shot to stable stratification, a buoyancy regime absent from training, correctly slowing mixing-layer growth. Together, our results show that foundation models can generalise well beyond their training data, predicting laboratory behavior and unseen physical regimes, opening new ways to probe longstanding simulation-experiment gaps.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as O(n^3) to O(n^7), with n proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting tahe potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

Existing video generation models excel at producing photo-realistic videos from text or images, but often lack physical plausibility and 3D controllability. To overcome these limitations, we introduce PhysCtrl, a novel framework for physics-grounded image-to-video generation with physical parameters and force control. At its core is a generative physics network that learns the distribution of physical dynamics across four materials (elastic, sand, plasticine, and rigid) via a diffusion model conditioned on physics parameters and applied forces. We represent physical dynamics as 3D point trajectories and train on a large-scale synthetic dataset of 550K animations generated by physics simulators. We enhance the diffusion model with a novel spatiotemporal attention block that emulates particle interactions and incorporates physics-based constraints during training to enforce physical plausibility. Experiments show that PhysCtrl generates realistic, physics-grounded motion trajectories which, when used to drive image-to-video models, yield high-fidelity, controllable videos that outperform existing methods in both visual quality and physical plausibility. Project Page: https://cwchenwang.github.io/physctrl

In an industrial group like Safran, numerical simulations of physical phenomena are integral to most design processes. At Safran's corporate research center, we enhance these processes by developing fast and reliable surrogate models for various physics. We focus here on two technologies developed in recent years. The first is a physical reduced-order modeling method for non-linear structural mechanics and thermal analysis, used for calculating the lifespan of high-pressure turbine blades and performing heat analysis of high-pressure compressors. The second technology involves learning physics simulations with non-parameterized geometrical variability using classical machine learning tools, such as Gaussian process regression. Finally, we present our contributions to the open-source and open-data community.

Reduction in effective spacetime dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wavefunction factors depend nontrivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a "covert" pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.

Text-to-video (T2V) models like Sora have made significant strides in visualizing complex prompts, which is increasingly viewed as a promising path towards constructing the universal world simulator. Cognitive psychologists believe that the foundation for achieving this goal is the ability to understand intuitive physics. However, the capacity of these models to accurately represent intuitive physics remains largely unexplored. To bridge this gap, we introduce PhyGenBench, a comprehensive Physics Generation Benchmark designed to evaluate physical commonsense correctness in T2V generation. PhyGenBench comprises 160 carefully crafted prompts across 27 distinct physical laws, spanning four fundamental domains, which could comprehensively assesses models' understanding of physical commonsense. Alongside PhyGenBench, we propose a novel evaluation framework called PhyGenEval. This framework employs a hierarchical evaluation structure utilizing appropriate advanced vision-language models and large language models to assess physical commonsense. Through PhyGenBench and PhyGenEval, we can conduct large-scale automated assessments of T2V models' understanding of physical commonsense, which align closely with human feedback. Our evaluation results and in-depth analysis demonstrate that current models struggle to generate videos that comply with physical commonsense. Moreover, simply scaling up models or employing prompt engineering techniques is insufficient to fully address the challenges presented by PhyGenBench (e.g., dynamic scenarios). We hope this study will inspire the community to prioritize the learning of physical commonsense in these models beyond entertainment applications. We will release the data and codes at https://github.com/OpenGVLab/PhyGenBench

Diffusion models can generate realistic videos, but existing methods rely on implicitly learning physical reasoning from large-scale text-video datasets, which is costly, difficult to scale, and still prone to producing implausible motions that violate fundamental physical laws. We introduce a training-free framework that improves physical plausibility at inference time by explicitly reasoning about implausibility and guiding the generation away from it. Specifically, we employ a lightweight physics-aware reasoning pipeline to construct counterfactual prompts that deliberately encode physics-violating behaviors. Then, we propose a novel Synchronized Decoupled Guidance (SDG) strategy, which leverages these prompts through synchronized directional normalization to counteract lagged suppression and trajectory-decoupled denoising to mitigate cumulative trajectory bias, ensuring that implausible content is suppressed immediately and consistently throughout denoising. Experiments across different physical domains show that our approach substantially enhances physical fidelity while maintaining photorealism, despite requiring no additional training. Ablation studies confirm the complementary effectiveness of both the physics-aware reasoning component and SDG. In particular, the aforementioned two designs of SDG are also individually validated to contribute critically to the suppression of implausible content and the overall gains in physical plausibility. This establishes a new and plug-and-play physics-aware paradigm for video generation.

Current video generation models cannot simulate physical consequences of 3D actions like forces and robotic manipulations, as they lack structural understanding of how actions affect 3D scenes. We present RealWonder, the first real-time system for action-conditioned video generation from a single image. Our key insight is using physics simulation as an intermediate bridge: instead of directly encoding continuous actions, we translate them through physics simulation into visual representations (optical flow and RGB) that video models can process. RealWonder integrates three components: 3D reconstruction from single images, physics simulation, and a distilled video generator requiring only 4 diffusion steps. Our system achieves 13.2 FPS at 480x832 resolution, enabling interactive exploration of forces, robot actions, and camera controls on rigid objects, deformable bodies, fluids, and granular materials. We envision RealWonder opens new opportunities to apply video models in immersive experiences, AR/VR, and robot learning. Our code and model weights are publicly available in our project website: https://liuwei283.github.io/RealWonder/

Recent advances in image and video generation raise hopes that these models possess world modeling capabilities, the ability to generate realistic, physically plausible videos. This could revolutionize applications in robotics, autonomous driving, and scientific simulation. However, before treating these models as world models, we must ask: Do they adhere to physical conservation laws? To answer this, we introduce Morpheus, a benchmark for evaluating video generation models on physical reasoning. It features 80 real-world videos capturing physical phenomena, guided by conservation laws. Since artificial generations lack ground truth, we assess physical plausibility using physics-informed metrics evaluated with respect to infallible conservation laws known per physical setting, leveraging advances in physics-informed neural networks and vision-language foundation models. Our findings reveal that even with advanced prompting and video conditioning, current models struggle to encode physical principles despite generating aesthetically pleasing videos. All data, leaderboard, and code are open-sourced at our project page.

No experimental test precludes the possibility that the dark matter experiences forces beyond general relativity -- in fact, a variety of cosmic microwave background observations suggest greater late-time structure than predicted in the standard Lambda cold dark matter model. We show that minimal models of scalar-mediated forces between dark matter particles do not enhance the growth of unbiased tracers of structure: weak lensing observables depend on the total density perturbation, for which the enhanced growth of the density contrast in the matter era is cancelled by the more rapid dilution of the background dark matter density. Moreover, the same background-level effects imply that scenarios compatible with CMB temperature and polarization anisotropies in fact suppress structure growth, as fixing the distance to last scattering requires a substantially increased density of dark energy. Though massive mediators undo these effects upon oscillating, they suppress structure even further because their gravitational impact as nonclustering subcomponents of matter outweighs the enhanced clustering strength of dark matter. We support these findings with analytic insight that clarifies the physical impact of dark forces and explains how primary CMB measurements calibrate the model's predictions for low-redshift observables. We discuss implications for neutrino mass limits and other cosmological anomalies, and we also consider how nonminimal extensions of the model might be engineered to enhance structure.

The origin of a chemical reaction between two reactant atoms is associated to the activation energy, with the assumption that, high-energy collisions between these atoms, are the ones that overcome the activation energy. Here, we (i) show that a stronger attractive van der Waals (vdW) and electron-ion Coulomb interactions between two polarized atoms are responsible to initiate a chemical reaction, either before or after the collision. We derive this stronger vdW attraction formula exactly using the quasi one-dimensional Drude model within the ionization energy theory and the energy-level spacing renormalization group method. Along the way, we (ii) expose the precise physical mechanism responsible for the existence of a stronger vdW interaction for both long and short distances, and also show how to technically avoid the electron-electron Coulomb repulsion between polarized electrons from these two reactant atoms. Finally, we properly and correctly associate the existence of this stronger attraction to Ramachandran's 'normal limits' (distance shorter than what is allowed by the standard vdW bond) between chemically nonbonded atoms.

We introduce PhysGaia, a novel physics-aware benchmark for Dynamic Novel View Synthesis (DyNVS) that encompasses both structured objects and unstructured physical phenomena. While existing datasets primarily focus on photorealistic appearance, PhysGaia is specifically designed to support physics-consistent dynamic reconstruction. Our benchmark features complex scenarios with rich multi-body interactions, where objects realistically collide and exchange forces. Furthermore, it incorporates a diverse range of materials, including liquid, gas, textile, and rheological substance, moving beyond the rigid-body assumptions prevalent in prior work. To ensure physical fidelity, all scenes in PhysGaia are generated using material-specific physics solvers that strictly adhere to fundamental physical laws. We provide comprehensive ground-truth information, including 3D particle trajectories and physical parameters (e.g., viscosity), enabling the quantitative evaluation of physical modeling. To facilitate research adoption, we also provide integration pipelines for recent 4D Gaussian Splatting models along with our dataset and their results. By addressing the critical shortage of physics-aware benchmarks, PhysGaia can significantly advance research in dynamic view synthesis, physics-based scene understanding, and the integration of deep learning with physical simulation, ultimately enabling more faithful reconstruction and interpretation of complex dynamic scenes.

Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding, received limited academic and industrial attention. This paper introduces PHYSICS, a dataset containing 16,568 high-quality physics problems spanning subjects and difficulty levels, to facilitate this issue. Specifically, PHYSICS is curated with exercises from over 100 textbooks through a carefully designed pipeline for quality control. It covers five major physics domains: Mechanics, Electromagnetism, Thermodynamics, Optics, and Modern Physics. It also spans a wide range of difficulty levels, from high school to graduate-level physics courses. To utilize the data for improving and evaluating the model's physical reasoning capabilities, we split the dataset into training and test sets, and provide reasoning paths generated by powerful reasoning models for the training data to facilitate model training. In addition, for the evaluation part, we find that existing evaluation frameworks exhibit biases in aspects such as units, simplification, and precision in physics domain. To balance efficiency and accuracy, we introduce a Rule+Model evaluation framework tailored to physics problems. Our evaluations on current state-of-the-art open-source and proprietary models highlight the limitations of current models in handling physics-related tasks. We hope that our dataset and evaluation methodology will jointly advance the development of LLMs in the field of physics.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, atomic physics, and optics. Each problem requires advanced physics knowledge and mathematical reasoning. We develop a robust automated evaluation system for precise and reliable validation. Our evaluation of leading foundation models reveals substantial limitations. Even the most advanced model, o3-mini, achieves only 59.9% accuracy, highlighting significant challenges in solving high-level scientific problems. Through comprehensive error analysis, exploration of diverse prompting strategies, and Retrieval-Augmented Generation (RAG)-based knowledge augmentation, we identify key areas for improvement, laying the foundation for future advancements.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a PDE identity in H2(R3), and we postulate ordering conditions for the PDE identity to define a Fredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing term belonging to L2(R3). As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layer of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive a Chemical Principle-like condition from the ordering conditions.

Sunspots survive on the solar surface for time-scales ranging from days to months. This requires them to be in an equilibrium involving magnetic fields and hydrodynamic forces. Unfortunately, theoretical models of sunspot equilibrium are very simplified as they assume that spots are static and possess a self-similar and axially symmetric magnetic field. These assumptions neglect the role of small scale variations of the magnetic field along the azimuthal direction produced by umbral dots, light bridges, penumbral filaments, and so forth. We aim at studying whether sunspot equilibrium is maintained once azimuthal fluctuations in the magnetic field, produced by the sunspot fine structure, are taken into account. To this end we apply the FIRTEZ Stokes inversion code to spectropolarimetric observations to infer the magnetic and thermodynamic parameters in two sunspots located at disk center and observed with two different instruments: one observed from the ground with the 1.5-meter German GREGOR Telescope and another with the Japanese spacecraft Hinode. We compare our results with three dimensional radiative magnetohydrodynamic simulations of a sunspot carried out with the MuRAM code. We infer clear variations in the gas pressure and density of the plasma directly related to fluctuations in the Lorentz force and associated with the filamentary structure in the penumbra. Similar results are obtained in the umbra despite its lack of observed filamentary structure. Results from the two observed sunspots are in excellent qualitative and quantitative agreement with the numerical simulations. Our results indicate that the magnetic topology of sunspots along the azimuthal direction is very close to magnetohydrostatic equilibrium, thereby helping to explain why sunspots are such long-lived structures capable of surviving on the solar surface for days or even full solar rotations.

The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the Stokes number, St_c, the amount of deposition has the unusual scaling law of exp(-1/(St-St_c)^{1/2}). The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time for the particle to reach the surface of the cylinder varying as 1/(St-St_c)^{1/2}, together with the distance away from the stagnation point (perpendicular to the flow direction) increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the amount of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

Recent advances in AI weather forecasting have led to the emergence of so-called "foundation models", typically defined by expensive pretraining and minimal fine-tuning for downstream tasks. However, in the natural sciences, a desirable foundation model should also encode meaningful statistical relationships between the underlying physical variables. This study evaluates the performance of the state-of-the-art Aurora foundation model in predicting hydrological variables, which were not considered during pretraining. We introduce a lightweight approach using shallow decoders trained on the latent representations of the pretrained model to predict these new variables. As a baseline, we compare this to fine-tuning the full model, which allows further optimization of the latent space while incorporating new variables into both inputs and outputs. The decoder-based approach requires 50% less training time and 35% less memory, while achieving strong accuracy across various hydrological variables and preserving desirable properties of the foundation model, such as autoregressive stability. Notably, decoder accuracy depends on the physical correlation between the new variables and those used during pretraining, indicating that Aurora's latent space captures meaningful physical relationships. In this sense, we argue that an important quality metric for foundation models in Earth sciences is their ability to be extended to new variables without a full fine-tuning. This provides a new perspective for making foundation models more accessible to communities with limited computational resources, while supporting broader adoption in Earth sciences.

Joint audio-video generation models are rapidly approaching professional production quality, raising a central question: do they understand audio-visual physics, or merely generate plausible sounds and frames that violate real-world consistency? We introduce AV-Phys Bench, a benchmark for evaluating physical commonsense in joint audio-video generation. AV-Phys Bench tests models across three scene categories: Steady State, Event Transition, and Environment Transition. It covers physics-grounded subcategories drawn from real-world scenes, plus Anti-AV-Physics prompts that deliberately request physically inconsistent audio-video behavior. Each generation is evaluated along five dimensions: visual semantic adherence, audio semantic adherence, visual physical commonsense, audio physical commonsense, and cross-modal physical commonsense. Across three proprietary and four open-source models, we find that Seedance 2.0 performs best overall, but all models remain far from robust physical understanding. Performance drops sharply on event-driven and environment-driven transitions, and even strong proprietary systems collapse on Anti-AV-Physics prompts. We further introduce AV-Phys Agent, a ReAct-style evaluator that combines a multimodal language model with deterministic acoustic measurement tools, producing rankings that closely align with human ratings. Our results identify cross-modal physical consistency and transition-driven scene dynamics as key open challenges for joint audio-video generation.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

We introduce adversarial learning methods for data-driven generative modeling of the dynamics of n^{th}-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. We introduce different formulations and training methods for learning models of stochastic dynamics based on observation of trajectory samples. We develop approaches using discriminators based on Maximum Mean Discrepancy (MMD), training protocols using conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. The adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.

Physical AI systems increasingly map multimodal observations, language instructions, and learned world representations into physically consequential actions. Robotics foundation models, vision-language-action models, and world-model-based autonomous systems can condition decisions that move vehicles, robots, drones, and industrial machines. This transition exposes a safety problem that is not fully captured by conventional AI content moderation or by classical robot safety alone: a black-box model may issue a physically consequential action while appearing confident, plausible, and semantically aligned. The resulting failure can be silent, arising from sensor drift, occlusion, state-estimation error, distribution shift, hallucinated affordances, or invalid physical assumptions before downstream hardware controllers detect a violation. Across embodied foundation models, world models, robotics simulation, embodied safety benchmarks, safe control, runtime assurance, uncertainty estimation, verification, and guardrail evaluation, model capability and safety mechanisms have advanced along largely separate technical tracks. A recurring gap synthesized here is that no single stream surveyed in this review supplies a complete runtime authorization boundary between black-box Physical AI models and physical execution. The resulting analysis develops a bounded problem formulation, a definition of silent physical-action failure, a taxonomy of runtime guardrail functions, and evaluation requirements for comparing guardrails as Physical AI assurance mechanisms.

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model -- and its qualitative and at times quantitative accuracy -- on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, and chemical reactions. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry.

Streaming video generation, as one fundamental component in interactive world models and neural game engines, aims to generate high-quality, low-latency, and temporally coherent long video streams. However, most existing work suffers from severe error accumulation that often significantly degrades the generated stream videos over long horizons. We design Rolling Forcing, a novel video generation technique that enables streaming long videos with minimal error accumulation. Rolling Forcing comes with three novel designs. First, instead of iteratively sampling individual frames, which accelerates error propagation, we design a joint denoising scheme that simultaneously denoises multiple frames with progressively increasing noise levels. This design relaxes the strict causality across adjacent frames, effectively suppressing error growth. Second, we introduce the attention sink mechanism into the long-horizon stream video generation task, which allows the model to keep key value states of initial frames as a global context anchor and thereby enhances long-term global consistency. Third, we design an efficient training algorithm that enables few-step distillation over largely extended denoising windows. This algorithm operates on non-overlapping windows and mitigates exposure bias conditioned on self-generated histories. Extensive experiments show that Rolling Forcing enables real-time streaming generation of multi-minute videos on a single GPU, with substantially reduced error accumulation.

Intuitive physics understanding in video diffusion models plays an essential role in building general-purpose physically plausible world simulators, yet accurately evaluating such capacity remains a challenging task due to the difficulty in disentangling physics correctness from visual appearance in generation. To the end, we introduce LikePhys, a training-free method that evaluates intuitive physics in video diffusion models by distinguishing physically valid and impossible videos using the denoising objective as an ELBO-based likelihood surrogate on a curated dataset of valid-invalid pairs. By testing on our constructed benchmark of twelve scenarios spanning over four physics domains, we show that our evaluation metric, Plausibility Preference Error (PPE), demonstrates strong alignment with human preference, outperforming state-of-the-art evaluator baselines. We then systematically benchmark intuitive physics understanding in current video diffusion models. Our study further analyses how model design and inference settings affect intuitive physics understanding and highlights domain-specific capacity variations across physical laws. Empirical results show that, despite current models struggling with complex and chaotic dynamics, there is a clear trend of improvement in physics understanding as model capacity and inference settings scale.

Trapped fields of over 20 T are, in principle, achievable in bulk, single-grain high temperature cuprate superconductors. The principle barriers to realizing such performance are, firstly, the large tensile stresses that develop during the magnetization of such trapped-field magnets as a result of the Lorentz force, which lead to brittle fracture of these ceramic-like materials at high fields and, secondly, catastrophic thermal instabilities as a result of flux movement during magnetization. Moreover, for a batch of samples nominally fabricated identically, the statistical nature of the failure mechanism means the best performance (i.e. trapped fields of over 17 T) cannot be attained reliably. The magnetization process, particularly to higher fields, also often damages the samples such that they cannot repeatedly trap high fields following subsequent magnetization. In this study, we report the sequential trapping of magnetic fields of ~ 17 T, achieving 16.8 T at 26 K initially and 17.6 T at 22.5 K subsequently, in a stack of two Ag-doped GdBa2Cu3O7-δ bulk superconductor composites of diameter 24 mm reinforced with (1) stainless-steel laminations, and (2) shrink-fit stainless steel rings. A trapped field of 17.6 T is, in fact, comparable with the highest trapped fields reported to date for bulk superconducting magnets of any mechanical and chemical composition, and this was achieved using the first composite stack to be fabricated by this technique.

Recent advances in foundation models, especially in large multi-modal models and conversational agents, have ignited interest in the potential of generally capable embodied agents. Such agents will require the ability to perform new tasks in many different real-world environments. However, current foundation models fail to accurately model physical interactions and are therefore insufficient for Embodied AI. The study of causality lends itself to the construction of veridical world models, which are crucial for accurately predicting the outcomes of possible interactions. This paper focuses on the prospects of building foundation world models for the upcoming generation of embodied agents and presents a novel viewpoint on the significance of causality within these. We posit that integrating causal considerations is vital to facilitating meaningful physical interactions with the world. Finally, we demystify misconceptions about causality in this context and present our outlook for future research.

The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in turbulence modeling, and many papers have produced unusable proposals either due to errors in math or physics, or to severe overfitting. We believe that "Turbulence Culture" (TC) takes years to learn and is difficult to convey especially considering the modern lack of time for careful study; important facts which are self-evident after a career in turbulence research and modeling and extensive reading are easy to miss. In addition, many of them are not absolute facts, a consequence of the gaps in our understanding of turbulence and the weak connection of models to first principles. Some of the mathematical facts are rigorous, but the physical aspects often are not. Turbulence models are surprisingly arbitrary. Disagreement between experts confuses the new entrants. In addition, several key properties of the models are ascertained through non-trivial analytical properties of the differential equations, which puts them out of reach of purely data-driven ML-type approaches. The best example is the crucial behavior of the model at the edge of the turbulent region (ETR). The knowledge we wish to put out here may be divided into "Mission" and "Requirements," each combining physics and mathematics. Clear lists of "Hard" and "Soft" constraints are presented. A concrete example of how DNS data could be used, possibly allied with ML, is first carried through and illustrates the large number of decisions needed. Our focus is on creating effective products which will empower CFD, rather than on publications.

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes. While neural operator frameworks, such as Deep Operator Networks (DeepONets), have shown considerable success in single-physics settings, their extension to multiphysics problems remains poorly understood. In particular, the challenge of learning nonlinear interactions between tightly coupled physical fields has received little systematic attention. This study addresses a foundational question: should the architectural design of a neural operator reflect the strength of physical coupling it aims to model? To answer this, we present the first comprehensive, architecture-aware evaluation of DeepONet variants across three regimes: single-physics, weakly coupled, and strongly coupled multiphysics systems. We consider a reaction-diffusion equation with dual spatial inputs, a nonlinear thermo-electrical problem with bidirectional coupling through temperature-dependent conductivity, and a viscoplastic thermo-mechanical model of steel solidification governed by transient phase-driven interactions. Two operator-learning frameworks, the classical DeepONet and its sequential GRU-based extension, S-DeepONet, are benchmarked using both single-branch and multi-branch (MIONet-style) architectures. Our results demonstrate that architectural alignment with physical coupling is crucial: single-branch networks significantly outperform multi-branch counterparts in strongly coupled settings, whereas multi-branch encodings offer advantages for decoupled or single-physics problems. Once trained, these surrogates achieve full-field predictions up to 1.8e4 times faster than high-fidelity finite-element solvers, without compromising solution accuracy.

Videos inherently represent 2D projections of a dynamic 3D world. However, our analysis suggests that video diffusion models trained solely on raw video data often fail to capture meaningful geometric-aware structure in their learned representations. To bridge this gap between video diffusion models and the underlying 3D nature of the physical world, we propose Geometry Forcing, a simple yet effective method that encourages video diffusion models to internalize latent 3D representations. Our key insight is to guide the model's intermediate representations toward geometry-aware structure by aligning them with features from a pretrained geometric foundation model. To this end, we introduce two complementary alignment objectives: Angular Alignment, which enforces directional consistency via cosine similarity, and Scale Alignment, which preserves scale-related information by regressing unnormalized geometric features from normalized diffusion representation. We evaluate Geometry Forcing on both camera view-conditioned and action-conditioned video generation tasks. Experimental results demonstrate that our method substantially improves visual quality and 3D consistency over the baseline methods. Project page: https://GeometryForcing.github.io.

Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy. Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/tum-pbs/SFBC.

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties during model training and effectively act as domain-specific regularizers of the empirical risk loss. Physics-informed neural networks is an example of this philosophy in which the outputs of deep neural networks are constrained to approximately satisfy a given set of partial differential equations. In this work we review recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data. We will also identify and analyze a fundamental mode of failure of such approaches that is related to numerical stiffness leading to unbalanced back-propagated gradients during model training. To address this limitation we present a learning rate annealing algorithm that utilizes gradient statistics during model training to balance the interplay between different terms in composite loss functions. We also propose a novel neural network architecture that is more resilient to such gradient pathologies. Taken together, our developments provide new insights into the training of constrained neural networks and consistently improve the predictive accuracy of physics-informed neural networks by a factor of 50-100x across a range of problems in computational physics. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/GradientPathologiesPINNs.

Many examples of cooperation exist in biology. In chemical systems however, which can sometimes be quite complex, we do not appear to observe intricate cooperative interactions. A key question for the origin of life, is then how can molecular cooperation first arise in an abiotic system prior to the emergence of biological replication. We postulate that selection at the molecular level is a driving force behind the complexification of chemical systems, particularly during the origins of life. In the theory of multilevel selection the two selective forces are: within-group and between-group, where the former tends to favor "selfish" replication of individuals and the latter favor cooperation between individuals enhancing the replication of the group as a whole. These forces can be quantified using the Price equation, which is a standard tool used in evolutionary biology to quantify evolutionary change. Our central claim is that replication and heredity in chemical systems are subject to selection, and quantifiable using the multilevel Price equation. We demonstrate this using the Graded Autocatalysis Replication Domain computer model, describing simple protocell composed out of molecules and its replication, which respectively analogue to the group and the individuals. In contrast to previous treatments of this model, we treat the lipid molecules themselves as replicating individuals and the protocells they form as groups of individuals. Our goal is to demonstrate how evolutionary biology tools and concepts can be applied in chemistry and we suggest that molecular cooperation may arise as a result of group selection. Further, the biological relation of parent-progeny is proposed to be analogue to the reactant-product relation in chemistry, thus allowing for tools from evolutionary biology to be applied to chemistry and would deepen the connection between chemistry and biology.

Predictive Physical AI systems output state rollouts, action chunks, and latent plans, yet a low root-mean-square error (RMSE) does not imply that a particular proposal is physically executable. We formulate physical admissibility as a prediction-control interface: before execution, a decoded proposal is treated as candidate dynamics and evaluated using kinematic, dynamic, and direct-to-composed horizon conditions. Passing is not a certificate of task success; rejection identifies violation of the specified physical envelope and gives a component-level reason. On Hugging Face LeRobot PushT, controlled falsification shows that one-step prediction-RMSE and standardized dynamics residuals reach area under the receiver operating characteristic curve (AUC) 0.982 and 0.972, kinematic-only conditions reach AUC 0.592, and the full gate reaches AUC 0.957 with condition-level attribution. In replay-based intervention experiments, residual-based filters and the full physical-admissibility gate prevent 87-$89% of invalid proposals while preserving mean progress near 0.998.

Foundation models are premised on the idea that sequence prediction can uncover deeper domain understanding, much like how Kepler's predictions of planetary motion later led to the discovery of Newtonian mechanics. However, evaluating whether these models truly capture deeper structure remains a challenge. We develop a technique for evaluating foundation models that examines how they adapt to synthetic datasets generated from some postulated world model. Our technique measures whether the foundation model's inductive bias aligns with the world model, and so we refer to it as an inductive bias probe. Across multiple domains, we find that foundation models can excel at their training tasks yet fail to develop inductive biases towards the underlying world model when adapted to new tasks. We particularly find that foundation models trained on orbital trajectories consistently fail to apply Newtonian mechanics when adapted to new physics tasks. Further analysis reveals that these models behave as if they develop task-specific heuristics that fail to generalize.

The relationship between balance laws and the Principle of Virtual Work as well as the structure of contact interactions in continua remain foundational issues in Mechanics. In this work, we revisit these issues within the distributional framework emphasized by Paul Germain. We show that while the Principle of Virtual Work implies balance of forces and moments for nth-gradient continua, balance laws alone do not suffice to characterize equilibrium for n geq 2. We then reexamine Noll's classical theorem asserting that surface contact forces depend solely on the unit normal to the surface and identify the precise role of his additional assumptions, namely the absence of edge and wedge contact interactions and the boundedness of the surface contact density on the space of oriented surfaces. We demonstrate that these hypotheses fail for general higher-gradient continua. Consequently, the presence of curvature-dependent surface contact forces in such materials does not conflict with Noll's theorem and refutes his claim of their nonexistence.

We discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that the underlying project of machine learning and the underlying project of physics are strongly coupled through the principle of sparsity, and we call upon theoretical physicists to work on AI as physicists. As a first step in that direction, we discuss an upcoming book on the principles of deep learning theory that attempts to realize this approach.

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally expensive to train and are subject to performance pitfalls, such as compounding errors during autoregressive rollout. In this work, we take a different perspective and look at scientific tasks further downstream of predicting the next frame, such as estimation of a system's governing physical parameters. Accuracy on these tasks offers a uniquely quantifiable glimpse into the physical relevance of the representations of these models. We evaluate the effectiveness of general-purpose self-supervised methods in learning physics-grounded representations that are useful for downstream scientific tasks. Surprisingly, we find that not all methods designed for physical modeling outperform generic self-supervised learning methods on these tasks, and methods that learn in the latent space (e.g., joint embedding predictive architectures, or JEPAs) outperform those optimizing pixel-level prediction objectives. Code is available at https://github.com/helenqu/physical-representation-learning.

We have investigated the effects of strain on two-dimensional square lattices and examined the methods for inducing pseudo-magnetic fields. In both the columnar and staggered pi-flux square lattices, we have found that strain only modulates Fermi velocities rather than inducing pseudo-magnetic fields. However, spatially non-uniform on-site potentials (anisotropic hoppings) can create pseudo-magnetic fields in columnar (staggered) pi-flux square lattices. On the other hand, we demonstrate that strain does induce pseudo-magnetic fields in staggered zero-flux square lattices. By breaking a quarter of the bonds, we clarify that a staggered zero-flux square lattice is topologically equivalent to a honeycomb lattice and displays pseudo-vector potentials and pseudo-Landau levels at the Dirac points.

It is demonstrated that self-diffusion and shear viscosity data for the TIP4P/Ice water model reported recently [L. Baran, W. Rzysko and L. MacDowell, J. Chem. Phys. {\bf 158}, 064503 (2023)] obey the microscopic version of the Stokes-Einstein relation without the hydrodynamic diameter.

LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility. We identify a data-induced failure mode, PhysHack, in which the assemblies satisfy physical-validity constraints while producing structures that are geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only a small fraction of the training data while improving physically grounded LEGO assembly generation. Building on the selected trajectories, we introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards. Our results show that physical validity alone is an insufficient proxy for reliable physical reasoning: models can learn to generate valid structures without preserving semantic or geometric fidelity. Experiments across model backbones and test-time scaling settings demonstrate that PVPO improves structural and semantic alignment, physical validity, structural stability, and calibration, while reducing reliance on extensive post-hoc rejection sampling. In particular, results on calibration show that PVPO mitigates PhysHack by making test-time selection more predictive of semantic and structural quality.

E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves - waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass-proportional to a3 in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Whittaker potential theory also offers a simple explanation for expansion of the universe - it is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space.

Recent advances in diffusion-based video generation have achieved remarkable visual realism but still struggle to obey basic physical laws such as gravity, inertia, and collision. Generated objects often move inconsistently across frames, exhibit implausible dynamics, or violate physical constraints, limiting the realism and reliability of AI-generated videos. We address this gap by introducing Physical Simulator In-the-loop Video Generation (PSIVG), a novel framework that integrates a physical simulator into the video diffusion process. Starting from a template video generated by a pre-trained diffusion model, PSIVG reconstructs the 4D scene and foreground object meshes, initializes them within a physical simulator, and generates physically consistent trajectories. These simulated trajectories are then used to guide the video generator toward spatio-temporally physically coherent motion. To further improve texture consistency during object movement, we propose a Test-Time Texture Consistency Optimization (TTCO) technique that adapts text and feature embeddings based on pixel correspondences from the simulator. Comprehensive experiments demonstrate that PSIVG produces videos that better adhere to real-world physics while preserving visual quality and diversity. Project Page: https://vcai.mpi-inf.mpg.de/projects/PSIVG/

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

We formulate nonequilibrium thermodynamics in which intensive variables acquire operational meaning through measurement protocols consistent with local reciprocity. Using physical equilibrium as a reference, conjugate observables are constructed by continuously adjusting devices along the local tangent space of the statistical manifold. In this relativity of observation, Onsager reciprocity holds locally, allowing inference-based Lagrange multipliers to be directly measured. This provides a systematic method to extend operational definitions of intensive variables to nonequilibrium states, highlighting their context-dependent nature and offering a concrete experimental strategy.

Sea ice is governed by highly complex, scale-invariant, and anisotropic processes that are challenging to represent in Earth system models. While advanced numerical models have improved our understanding of the sea-ice dynamics, their computational costs often limit their application in ensemble forecasting and climate simulations. Here, we introduce GenSIM, the first generative AI-based pan-Arctic model that predicts the evolution of all relevant key properties, including concentration, thickness, and drift, in a 12-hour window with improved accuracy over deterministic predictions and high computational efficiency, while remaining physically consistent. Trained on a long simulation from a state-of-the-art sea-ice--ocean system, GenSIM robustly reproduces statistics as observed in numerical models and observations, exhibiting brittle-like short-term dynamics while also depicting the long-term sea-ice decline. Driven solely by atmospheric forcings, we attribute GenSIM's emergent extrapolation capabilities to patterns that reflect the long-term impact of the ocean: it seemingly has learned an internal ocean emulator. This ability to infer slowly evolving climate-relevant dynamics from short-term predictions underlines the large potential of generative models to generalise for unseen climates and to encode hidden physics.

Generating physically realistic 3D molecular structures remains a core challenge in molecular generative modeling. While diffusion models equipped with equivariant neural networks have made progress in capturing molecular geometries, they often struggle to produce equilibrium structures that adhere to physical principles such as force field consistency. To bridge this gap, we propose Reinforcement Learning with Physical Feedback (RLPF), a novel framework that extends Denoising Diffusion Policy Optimization to 3D molecular generation. RLPF formulates the task as a Markov decision process and applies proximal policy optimization to fine-tune equivariant diffusion models. Crucially, RLPF introduces reward functions derived from force-field evaluations, providing direct physical feedback to guide the generation toward energetically stable and physically meaningful structures. Experiments on the QM9 and GEOM-drug datasets demonstrate that RLPF significantly improves molecular stability compared to existing methods. These results highlight the value of incorporating physics-based feedback into generative modeling. The code is available at: https://github.com/ZhijianZhou/RLPF/tree/verl_diffusion.

In this paper, we evaluate the Casimir energy and pressure for a massive fermionic field confined in the region between two parallel plates. In order to implement this confinement we impose the standard MIT bag boundary on the plates for the fermionic field. In this paper we consider a quantum field theory model with a CPT even, aether-like Lorentz symmetry violation. It turns out that the fermionic Casimir energy and pressure depend on the direction of the constant vector that implements the Lorentz symmetry breaking.

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.

Effectively leveraging data from multiple quantum-chemical methods is essential for building machine-learned force fields (MLFFs) that are applicable to a wide range of chemical systems. This study systematically investigates two multi-fidelity training strategies, pre-training/fine-tuning and multi-headed training, to elucidate the mechanisms underpinning their success. We identify key factors driving the efficacy of pre-training followed by fine-tuning, but find that internal representations learned during pre-training are inherently method-specific, requiring adaptation of the model backbone during fine-tuning. Multi-headed models offer an extensible alternative, enabling simultaneous training on multiple fidelities. We demonstrate that a multi-headed model learns method-agnostic representations that allow for accurate predictions across multiple label sources. While this approach introduces a slight accuracy compromise compared to sequential fine-tuning, it unlocks new cost-efficient data generation strategies and paves the way towards developing universal MLFFs.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the AdS/CFT correspondence by solving the Einstein-Abelian-Higgs model in an AdS_4 black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient local ordering episodes with switching rules (a volatile Maxwell-demon effect). We illustrate entropy growth with a two-region toy model (organizer vs. play area), where entropy production is nonnegative and long-time behavior is typically play-area dominated. We also model toy diffusion and curiosity-driven behavior, where novelty matters more than punishment in the short term, while gradual learning still occurs.

Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy-force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves 40% lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to 20times lower energy MAE. On QH9, QHFlow2 reduces energy error by up to 20times compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations.

Denoising diffusion models hold great promise for generating diverse and realistic human motions. However, existing motion diffusion models largely disregard the laws of physics in the diffusion process and often generate physically-implausible motions with pronounced artifacts such as floating, foot sliding, and ground penetration. This seriously impacts the quality of generated motions and limits their real-world application. To address this issue, we present a novel physics-guided motion diffusion model (PhysDiff), which incorporates physical constraints into the diffusion process. Specifically, we propose a physics-based motion projection module that uses motion imitation in a physics simulator to project the denoised motion of a diffusion step to a physically-plausible motion. The projected motion is further used in the next diffusion step to guide the denoising diffusion process. Intuitively, the use of physics in our model iteratively pulls the motion toward a physically-plausible space, which cannot be achieved by simple post-processing. Experiments on large-scale human motion datasets show that our approach achieves state-of-the-art motion quality and improves physical plausibility drastically (>78% for all datasets).