Daily Papers

Advancing physics reasoning in large language models requires scalable training data that connect physical laws, concrete problem scenarios, and verifiable numerical answers. Expert-designed problems offer top-down control over physical laws, conditions, and scenarios, but require costly human effort. LLM-based synthesis from texts scales efficiently, but model-generated answers and assessments leave supervision vulnerable to hallucinations. We introduce TIRE, a framework for Top-Down Formula Instantiation with Reliable Execution that brings knowledge-driven problem construction to large-scale data generation. Top-down instantiation uses reusable physical formulas and their applicability conditions to control the physical relations and numerical configurations of generated problems. Reliable execution establishes reference answers before problem generation, providing a common numerical foundation for problem construction and teacher distillation. Together, these mechanisms combine control over problem content with execution-grounded supervision for both supervised fine-tuning and reinforcement learning. Using TIRE, we construct TIRE-19k, spanning nine subfields of physics. Across 3 backbone LLMs and 4 benchmarks, TIRE-19k outperforms 5 representative datasets with equal amounts of SFT data, exceeding the strongest baseline by 2.86 percentage points on average. Further GRPO raises Qwen3-8B's average accuracy by 1.52 percentage points over its TIRE-19k SFT checkpoint. These results demonstrate the value of generating physics training data from explicit physical knowledge with reliable execution.

Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation (R^2 approx 0.95) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.

The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we introduce FormulaReasoning, a new benchmark for formula-based numerical reasoning comprising 5,324 questions requiring calculations grounded in external physics principles. We provide high-quality, fine-grained annotations in English and Chinese--including formula structures, parameter names, symbols, values, and units--curated through manual effort and LLM-assisted validation. Additionally, we provide a consolidated formula database as an external knowledge source. To further challenge model performance, we develop an extended version of the dataset by coupling multiple questions. We evaluate various architectural and methodological frameworks, including retrieval-augmented methods, modular reasoning (formula generation, parameter extraction, and calculation), and preference-based optimization. Our analysis identifies critical challenges in formula-based reasoning, highlighting significant opportunities for future methodological advancement.

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help experimental physicist to perform the data analysis. As an example, we show how to use these formulae to distinguish the different mechanisms of e+pto e+J/ψ+ p process for searching the signals of P_c states at the energy region of Electron-Ion collider at China (EicC).

The operation of replacing every vertex of an r-regular lattice H by a complete graph of order r is called clique-inserting, and the resulting lattice is called the clique-inserted-lattice of H. For any given r-regular lattice, applying this operation iteratively, an infinite family of r-regular lattices is generated. Some interesting lattices including the 3-12-12 lattice can be constructed this way. In this paper, we reveal the relationship between the energy and resistance distance of an r-regular lattice and that of its clique-inserted-lattice. As an application, the asymptotic energy per vertex and average resistance distance of the 3-12-12 and 3-6-24 lattices are computed. We also give formulae expressing the numbers of spanning trees and dimers of the k-th iterated clique-inserted lattices in terms of that of the original lattice. Moreover, we show that new families of expander graphs can be constructed from the known ones by clique-inserting.

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.

Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing and understanding natural language, they encounter challenges with mathematical notation, which involves a complex structure and diverse representations. This study focuses on the development of specialized training datasets to enhance the encoding of mathematical content. We introduce Math Mutator (MAMUT), a framework capable of generating equivalent and falsified versions of a given mathematical formula in LaTeX notation, effectively capturing the mathematical variety in notation of the same concept. Based on MAMUT, we have generated four large mathematical datasets containing diverse notation, which can be used to train language models with enhanced mathematical embeddings.

Physics reasoning requires constructing a consistent model of the underlying physical system rather than relying solely on symbolic or formula-based manipulation. Although large language models have shown strong ability in solving math and coding problems, they still struggle with physics problems, as these problems entangle the physical modeling process with mathematical calculations. Humans approach physics by first building a representation of the system before performing calculations. Inspired by this, we introduce a unified framework that distills intermediate representations that explicitly encode the physical modeling process and adopt a two-stage post-training strategy, where supervised fine-tuning establishes structured modeling, and reinforcement learning with rubric-based feedback improves the quality of the modeling process. Experiments on multiple multimodal physics benchmarks show that our approach leads to consistent improvements in reasoning performance across different models and datasets. On PhysReason, PhyX and SeePhys benchmarks, physical modeling output performs GRPO by an average ~3%, showing that explicit physical modeling is an efficient strategy of improving physics reasoning for small LLMs.

Text-to-image generation has reached photorealistic quality, yet state-of-the-art systems remain unreliable at producing scientific diagrams, whose value depends not on appearance but on physical faithfulness: correct force directions, valid coordinate systems, consistent thermodynamic states, and equations matching the depicted scenario. Trained on web imagery with physically shallow captions, generic models produce diagrams that look plausible but are physically wrong, harmful in education and scientific communication. We present Princigram, a physics-faithful scientific-diagram generator, and its data pipeline. Our central advance is Structured Physical Chain-of-Thought (SP-CoT): a per-subdiscipline schema that decomposes a physics diagram into an explicit multi-step reasoning chain across six subdisciplines, from scene identification through force or process analysis to governing laws and synthesis. Unlike free-form chain-of-thought, SP-CoT follows a fixed schema with strict fidelity rules that separate visually grounded facts from physically inferred reasoning and type all mathematics symbolically; it serves both as dense training supervision and, at inference, as a structured "thinking" prompt. With it we curate and structurally annotate 4.3 million physics images, of which 115,037 carry expert-level annotation, and adapt a unified multimodal backbone. We further introduce VeriphyT2IBench, whose questions are derived from each held-out diagram's own structured annotation: each diagram becomes an item-specific bank of binary questions about its objects, forces, and states, so a judge model's score decomposes into named physical facts rather than one holistic number. On the physics subset of GenExam and on VeriphyT2IBench, Princigram shows that explicit physics-structured supervision improves the physical faithfulness of generated scientific diagrams.

Correctly parsing mathematical formulas from PDFs is critical for training large language models and building scientific knowledge bases from academic literature, yet existing benchmarks either exclude formulas entirely or lack semantically-aware evaluation metrics. We introduce a novel benchmarking framework centered on synthetically generated PDFs with precise LaTeX ground truth, enabling systematic control over layout, formulas, and content characteristics. A key methodological contribution is pioneering LLM-as-a-judge for semantic formula assessment, combined with a robust two-stage matching pipeline that handles parser output inconsistencies. Through human validation on 250 formula pairs (750 ratings from 30 evaluators), we demonstrate that LLM-based evaluation achieves substantially higher correlation with human judgment (Pearson r=0.78) compared to CDM (r=0.34) and text similarity (r~0). Evaluating 20+ contemporary PDF parsers (including specialized OCR models, vision-language models, and rule-based approaches) across 100 synthetic documents with 2,000+ formulas reveals significant performance disparities. Our findings provide crucial insights for practitioners selecting parsers for downstream applications and establish a robust, scalable methodology that enables reproducible evaluation of PDF formula extraction quality. Code and benchmark data: https://github.com/phorn1/pdf-parse-bench

We introduce PHYBench, a novel, high-quality benchmark designed for evaluating reasoning capabilities of large language models (LLMs) in physical contexts. PHYBench consists of 500 meticulously curated physics problems based on real-world physical scenarios, designed to assess the ability of models to understand and reason about realistic physical processes. Covering mechanics, electromagnetism, thermodynamics, optics, modern physics, and advanced physics, the benchmark spans difficulty levels from high school exercises to undergraduate problems and Physics Olympiad challenges. Additionally, we propose the Expression Edit Distance (EED) Score, a novel evaluation metric based on the edit distance between mathematical expressions, which effectively captures differences in model reasoning processes and results beyond traditional binary scoring methods. We evaluate various LLMs on PHYBench and compare their performance with human experts. Our results reveal that even state-of-the-art reasoning models significantly lag behind human experts, highlighting their limitations and the need for improvement in complex physical reasoning scenarios. Our benchmark results and dataset are publicly available at https://phybench-official.github.io/phybench-demo/.

The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide foundation models and sophisticated agentic systems pushing the boundaries of formal mathematical reasoning to approach the natural language capability of LLMs. However, little attention has been given to the formal physics reasoning, which also heavily relies on similar problem-solving and theorem-proving frameworks. To solve this problem, this paper presents, to the best of our knowledge, the first approach to enhance formal theorem proving in the physics domain. We compose a dedicated dataset PhysLeanData for the task. It is composed of theorems sampled from PhysLean and data generated by a conjecture-based formal data generation pipeline. In the training pipeline, we leverage DeepSeek-Prover-V2-7B, a strong open-source mathematical theorem prover, and apply Reinforcement Learning with Verifiable Rewards (RLVR) to train our model PhysProver. Comprehensive experiments demonstrate that, using only sim5K training samples, PhysProver achieves an overall 2.4\% improvement in multiple sub-domains. Furthermore, after formal physics training, we observe 1.3\% gains on the MiniF2F-Test benchmark, which indicates non-trivial generalization beyond physics domains and enhancement for formal math capability as well. The results highlight the effectiveness and efficiency of our approach, which provides a paradigm for extending formal provers outside mathematical domains. To foster further research, we will release both our dataset and model to the community.

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.

Formula recognition is an important task in document intelligence. It involves converting mathematical expressions from document images into structured symbolic formats that computers can easily work with. LaTeX is the most common format used for this purpose. In this work, we present PP-FormulaNet, a state-of-the-art formula recognition model that excels in both accuracy and efficiency. To meet the diverse needs of applications, we have developed two specialized models: PP-FormulaNet-L, tailored for high-accuracy scenarios, and PP-FormulaNet-S, optimized for high-efficiency contexts. Our extensive evaluations reveal that PP-FormulaNet-L attains accuracy levels that surpass those of prominent models such as UniMERNet by a significant 6%. Conversely, PP-FormulaNet-S operates at speeds that are over 16 times faster. These advancements facilitate seamless integration of PP-FormulaNet into a broad spectrum of document processing environments that involve intricate mathematical formulas. Furthermore, we introduce a Formula Mining System, which is capable of extracting a vast amount of high-quality formula data. This system further enhances the robustness and applicability of our formula recognition model. Code and models are publicly available at PaddleOCR(https://github.com/PaddlePaddle/PaddleOCR) and PaddleX(https://github.com/PaddlePaddle/PaddleX).

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for pi, ln(2), Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

Large language models (LLMs) have rapidly advanced and are increasingly capable of tackling complex scientific problems, including those in physics. Despite this progress, current LLMs often fail to emulate the concise, principle-based reasoning characteristic of human experts, instead generating lengthy and opaque solutions. This discrepancy highlights a crucial gap in their ability to apply core physical principles for efficient and interpretable problem solving. To systematically investigate this limitation, we introduce PhySense, a novel principle-based physics reasoning benchmark designed to be easily solvable by experts using guiding principles, yet deceptively difficult for LLMs without principle-first reasoning. Our evaluation across multiple state-of-the-art LLMs and prompt types reveals a consistent failure to align with expert-like reasoning paths, providing insights for developing AI systems with efficient, robust and interpretable principle-based scientific reasoning.

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.

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.

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.

Generating physics diagrams from text requires strict adherence to physical laws. While current generative models produce visually plausible outputs, they systematically hallucinate force vectors, ignore conservation laws, and violate geometric constraints. We present PhyDrawGen, a neuro-symbolic pipeline that decouples semantic scene understanding from physical constraint satisfaction. First, a large language model extracts a typed scene graph from the problem text. A deterministic solver then converts this graph into a Planar Straight-Line Graph (PSLG), encoding force balance, optical paths, and field topologies as exact geometric primitives. Finally, a fine-tuned Qwen-VL model implements a visually grounded propose-verify loop to iteratively correct any constraint violations. Evaluated on a benchmark of 1,449 problems spanning mechanics, optics, and electromagnetism, PhyDrawGen significantly outperforms GPT-5-image, Gemini 2.5 Flash, and Gemini 3 Pro, demonstrating robust physical accuracy even on unusual-object problems.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the star-exponential with the quantum propagator for bosonic systems, this work develops the analogous extension for the fermionic case. A rigorous method, based on Grassmann variables and coherent states, is constructed to obtain a closed-form expression for the fermionic star-exponential from its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, allowing for the calculation of the ground state energy directly in phase space. Finally, the method is validated by successfully applying it to the simple and driven harmonic oscillators, where it is demonstrated that a simplified ("naive") approach (with an ad-hoc "remediation") is a valid weak-coupling limit of the rigorous ("meticulous") formalism, thereby providing a new and powerful computational tool for the study of fermionic systems.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

Extracting the London penetration depth, λ(T), from the measured magnetic susceptibility, χ(T), of a superconducting platelet in a perpendicular magnetic field requires knowing the function χ(λ) computed for the actual sample geometry. Thin films are increasingly important in quantum computing and superconducting electronics, most of which operate at ultra-low excitation fields in the vortex-free regime. Understanding their electromagnetic response in the Meissner--London (finite-λ, no vortices) state is therefore essential for extracting intrinsic properties such as the London penetration depth and superfluid phase stiffness. While numerous prior works have addressed different aspects of this problem, here we focus on providing an analytical semi-empirical representation of χ(λ) based on the 2D sheet-current model and establishing the limits of its applicability using two independent full 3D numerical solutions: finite-element modeling and a volume-current integral equation. As a result, we provide χ(λ) for a disc of radius a and thickness d in closed form, valid for all λ and for aspect ratios δequiv d/(2a)le0.05, and accurate to 0.1%. The two-dimensional sheet description with Pearl length Λ=2λ^2/d is adequate for δlesssim10^{-4} and λgtrsim 4d. Thicker films require the full closed form, which includes the three-dimensional corrections. Using the same numerical analysis, we provide an empirical formula that maps rectangular samples---the geometry most commonly used in experiments---onto a disc with an ``effective radius'' for subsequent calculation of χ(λ), and formulate a complete calibration protocol for whole-sample susceptibility measurements.

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/.

Predicting the relationship between surface charge density and electrostatic potential for spherical particles remains a fundamental challenge in colloid science. Because the governing non-linear Poisson--Boltzmann equation lacks a general exact analytical solution, researchers typically rely on numerical calculations or various semi-empirical approximations. In this paper, we overcome these limitations by developing a dual-asymptotic framework that provides explicit, closed-form expressions for this surface charge--potential relationship across the entire spectrum of particle curvature. For weakly curved systems, where the Debye length λ_D is much smaller than the particle radius R (λ_D/R ll 1), a formal mathematical derivation rigorously establishes the Ohshima--Healy--White formula as an exact regular perturbation expansion. Conversely, for highly curved spheres (R/λ_D ll 1), we employ singular perturbation analysis using the scaled particle radius as the small parameter. This approach provides a first-principles mathematical justification for the spherical Debye--Hückel theory, proving that its leading-order expansion remains asymptotically exact within the full non-linear Poisson--Boltzmann framework due to the geometric deactivation of non-linearity. Crucially, we map the exact limits of this geometric regulation, demonstrating how non-linear screening re-emerges as the particle radius increases, with the breakdown threshold governed by the interplay between curvature and surface charge density.

Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for Gaussian and mildly non-Gaussian fields. In this paper we extend the formulae to composite fields which are sums of two fields and explicitly derive the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian fields. These formulae are applicable to observed data which is usually a sum of the true signal and one or more secondary fields that can be either noise, or some residual contaminating signal. Our formulae provide explicit quantification of the effect of the secondary field on the morphology and statistical nature of the true signal. As examples, we apply the formulae to determine how the presence of Gaussian noise can bias the morphological properties and statistical nature of Gaussian and non-Gaussian CMB temperature maps.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.

Predicting physical properties of materials from their crystal structures is a fundamental problem in materials science. In peripheral areas such as the prediction of molecular properties, fully connected attention networks have been shown to be successful. However, unlike these finite atom arrangements, crystal structures are infinitely repeating, periodic arrangements of atoms, whose fully connected attention results in infinitely connected attention. In this work, we show that this infinitely connected attention can lead to a computationally tractable formulation, interpreted as neural potential summation, that performs infinite interatomic potential summations in a deeply learned feature space. We then propose a simple yet effective Transformer-based encoder architecture for crystal structures called Crystalformer. Compared to an existing Transformer-based model, the proposed model requires only 29.4% of the number of parameters, with minimal modifications to the original Transformer architecture. Despite the architectural simplicity, the proposed method outperforms state-of-the-art methods for various property regression tasks on the Materials Project and JARVIS-DFT datasets.

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms H_c, {He_c}^+ and {Li_c}^{2+} confined by an impenetrable spherical box. Novel expressions for entropic uncertainty relation and Shannon entropies S_r and S_p are proposed to ensure their physical dimensionless characteristic. The electronic ground state energy and the quantities S_r, S_p and S_t are calculated for the hydrogenic-like atoms to different confinement radii by using a variational method. The global behavior of these quantities and different conjectures are analyzed. The results are compared, when available, with those previously published.

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.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

Generative modeling has emerged as a promising approach for crystal structure discovery. However, existing LLM-based generative models struggle with low-level atomic precision, while diffusion-based methods fall short in integrating high-level scientific knowledge. As a result, generated structures are often invalid, unstable, or do not possess desirable properties. To address this gap, we propose CrystalReasoner (\method), an end-to-end LLM framework that generates crystal structures from natural language instructions through reasoning and alignment. \method introduces physical priors as thinking tokens, which include crystallographic symmetry, local coordination environments and predicted physical properties before generating atomic coordinates. This bridges the gap between natural language and 3D structures. \method then employs reinforcement learning (RL) with a multi-objective, dense reward function to align generation with physical validity, chemical consistency, and thermodynamic stability. For property-conditioned tasks, we design task-specific reward functions and train specialized models for discrete constraints (e.g., space group) and continuous properties (e.g., elasticity, thermal expansion). Empirical results demonstrate that compared to prior works and baselines without thinking traces or RL, \method obtains better performance on diverse metrics, triples S.U.N. ratio, and achieves better performance for property conditioned generation. \method also exhibits adaptive reasoning, increasing reasoning lengths as the number of atoms increases. Our work demonstrates the potential of leveraging thinking traces and RL for generating valid, stable, and property-conditioned crystal structures. Please see our work at https://crystalreasoner.github.io/ .

This lecture presents an overview of the basic concepts and fundamentals of Engineering Materials within the framework of accelerator applications. After a short introduction, main concepts relative to the structure of matter are reviewed, like crystalline structures, defects and dislocations, phase diagrams and transformations. The microscopic description is correlated with physical properties of materials, focusing in metallurgical aspects like deformation and strengthening. Main groups of materials are addressed and described, namely, metals and alloys, ceramics, polymers, composite materials, and advanced materials, where brush-strokes of tangible applications in particle accelerators and detectors are given. Deterioration aspects of materials are also presented, like corrosion in metals and degradation in plastics.

We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern' recognition, we developed the Newton physics-based NS scheme. Once the force pattern is confirmed, the neuro network simply does the checking of the 'pattern stability' instead of the continuous fitting by computational resource consuming big data-driven processing. In the given physics's law system, once the field is confirmed, the mathematics bases for the force field description actually are not diverged but denumerable, which can save the function representations from the exhaustible available mathematics bases. In this work, we endorsed Newton's Law into the deep learning technology and proposed Newton Scheme (NS). Under NS, the user first identifies the path pattern, like the constant acceleration movement.The object recognition technology first loads mass information, then, the NS finds the matched physical pattern and describe and predict the trajectory of the movements with nearly zero error. We compare the major contribution of this NS with the TCN, GRU and other physics inspired 'FIND-PDE' methods to demonstrate fundamental and extended applications of how the NS works for the free-falling, pendulum and curve soccer balls.The NS methodology provides more opportunity for the future deep learning advances.

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.

Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. Recently, large language models (LLMs) have emerged as promising tools for symbolic equation discovery, owing to their broad domain knowledge and strong reasoning capabilities. However, most existing LLM-based systems try to guess equations directly from data, without modeling the multi-step reasoning process that scientists often follow: first inferring physical properties such as symmetries, then using these as priors to restrict the space of candidate equations. We introduce KeplerAgent, an agentic framework that explicitly follows this scientific reasoning process. The agent coordinates physics-based tools to extract intermediate structure and uses these results to configure symbolic regression engines such as PySINDy and PySR, including their function libraries and structural constraints. Across a suite of physical equation benchmarks, KeplerAgent achieves substantially higher symbolic accuracy and greater robustness to noisy data than both LLM and traditional baselines.

Spreadsheets are widely recognized as the most popular end-user programming tools, which blend the power of formula-based computation, with an intuitive table-based interface. Today, spreadsheets are used by billions of users to manipulate tables, most of whom are neither database experts nor professional programmers. Despite the success of spreadsheets, authoring complex formulas remains challenging, as non-technical users need to look up and understand non-trivial formula syntax. To address this pain point, we leverage the observation that there is often an abundance of similar-looking spreadsheets in the same organization, which not only have similar data, but also share similar computation logic encoded as formulas. We develop an Auto-Formula system that can accurately predict formulas that users want to author in a target spreadsheet cell, by learning and adapting formulas that already exist in similar spreadsheets, using contrastive-learning techniques inspired by "similar-face recognition" from compute vision. Extensive evaluations on over 2K test formulas extracted from real enterprise spreadsheets show the effectiveness of Auto-Formula over alternatives. Our benchmark data is available at https://github.com/microsoft/Auto-Formula to facilitate future research.

Recently, the physical capabilities of (M)LLMs have garnered increasing attention. However, existing benchmarks for physics suffer from two major gaps: they neither provide systematic and up-to-date coverage of real-world physics competitions such as physics Olympiads, nor enable direct performance comparison with humans. To bridge these gaps, we present HiPhO, the first benchmark dedicated to high school physics Olympiads with human-aligned evaluation. Specifically, HiPhO highlights three key innovations. (1) Comprehensive Data: It compiles 13 latest Olympiad exams from 2024-2025, spanning both international and regional competitions, and covering mixed modalities that encompass problems spanning text-only to diagram-based. (2) Professional Evaluation: We adopt official marking schemes to perform fine-grained grading at both the answer and step level, fully aligned with human examiners to ensure high-quality and domain-specific evaluation. (3) Comparison with Human Contestants: We assign gold, silver, and bronze medals to models based on official medal thresholds, thereby enabling direct comparison between (M)LLMs and human contestants. Our large-scale evaluation of 30 state-of-the-art (M)LLMs shows that: across 13 exams, open-source MLLMs mostly remain at or below the bronze level; open-source LLMs show promising progress with occasional golds; closed-source reasoning MLLMs can achieve 6 to 12 gold medals; and most models still have a significant gap from full marks. These results highlight a substantial performance gap between open-source models and top students, the strong physical reasoning capabilities of closed-source reasoning models, and the fact that there is still significant room for improvement. HiPhO, as a rigorous, human-aligned, and Olympiad-focused benchmark for advancing multimodal physical reasoning, is open-source and available at https://github.com/SciYu/HiPhO.

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through extensive experiments, we show that explicit incorporation of fundamental physics knowledge significantly strengthens the generalization ability of neural operators. We will release models and codes at https://sites.google.com/view/sciml-fundemental-pde.

The study demonstrates the capabilities of a vector-based approach for calculating stoichiometric coefficients in chemical equations, using black powder as an illustrative example. A method is proposed for selecting and constraining intermediate interactions between reactants, as well as for identifying final products. It is shown that even a small number of components can lead to a large number of final and intermediate products. Through concrete calculations, a correlation is established between the number of possible chemical equations and the number of reactants. A methodology is proposed for computing all possible chemical equations within a reaction system for arbitrary component ratios, enabling the derivation of all feasible chemical reactions. Additionally, a method is developed for calculating the chemical composition for a fixed set of reactants, allowing for the evaluation of the set of products resulting from all possible chemical interactions given a specified initial composition.

Advanced table question answering (TableQA) methods prompt large language models (LLMs) to generate answer text, SQL query, Python code, or custom operation, which impressively improve the complex reasoning problems in the TableQA task. However, these methods lack the versatility to cope with specific question types or table structures. In contrast, the Spreadsheet Formula, the widely used and well-defined operation language for tabular data, has not been thoroughly explored to solve TableQA. In this paper, we first attempt to use the Formula as the executable representation for solving complex reasoning on tables with different structures. Specifically, we construct FromulaQA, a large Formula-annotated TableQA dataset from existing datasets. In addition, we propose TabAF, a general table answering framework to solve multiple types of tasks over multiple types of tables simultaneously, which decodes answers and Formulas with a single LLM backbone. Extensive experiments demonstrate the versatility and generalization of TabAF. Under the same model size, TabAF achieves new state-of-the-art performance on the WikiTableQuestion, HiTab, and TabFact.

Let P_h be a semiclassical pseudodifferential operator on a closed Riemannian manifold (M,g), with principal symbol p. We consider perturbations P_h+h^αQ, with 0<αle 1, where Q is a semiclassical pseudodifferential operator whose symbol oscillates at scale h^β, with 2β<α. Assuming that the classical dynamics of the unperturbed system on a regular energy surface p^{-1}(E) is hyperbolic, we prove a Gutzwiller trace formula for the perturbed operator that holds up to times of order |log h|. This formula relates the distribution of energy levels of the quantum system near the energy E to the periodic orbits of its classical counterpart. The perturbation h^αQ affects only the phases appearing in the trace formula.

We derive the gravitational radiation generated by a localised matter source in de Sitter spacetime at octupolar order in the multipolar expansion, working in generalised harmonic gauge in the future Poincaré patch. The scalar, vector, and tensor perturbation equations are solved explicitly, taking into account the cosmological tail. This constitutes the first extension of the de Sitter multipolar expansion beyond quadrupolar order. A key technical ingredient is a universal multipole moment differentiation identity, which unifies the relations between multipole moments into a single recursive formula and enables a controlled extension to higher multipoles. Using the symmetric trace-free tensor formalism of Blanchet, Damour, and Iyer, we further develop a systematic translation of the radiative solution into a spherical harmonic basis, and apply it to both the quadrupolar and octupolar metric perturbations. This representation renders the angular structure of the radiation manifest, simplifies the verification of the linearised field equations, and facilitates direct comparison with Bondi-gauge and other perturbative treatments of de Sitter spacetime.

Video world models are expected to predict how the physical world evolves, yet they often produce visually plausible videos that violate basic physical principles. Existing approaches commonly assume that natural language is insufficient to represent the physical knowledge required for reliable generation, and therefore introduce additional visual, latent, numerical, or planning-based signals. We revisit this assumption and introduce Physis-Lang, a self-evolving framework that treats physical language as a shared and optimizable representation across data curation, model training, and video generation. Physis-Lang represents physical processes through language that describes their relevant entities, causes, interactions, governing principles, temporal evolution, and effects. To improve this representation, we construct PhysCapBench, which decomposes physical processes into atomic assertions and evaluates captions using recall and precision. An agentic loop iteratively analyzes assertion-level errors and refines the instruction used to produce physical captions. Physis-Lang further converts model deficiencies into textual descriptions and uses language-guided retrieval to identify visually diverse videos that cover missing physical processes. Experiments on four widely used physical video benchmarks with Wan and Cosmos backbones demonstrate consistent improvements in physical plausibility. Notably, starting from open-source Cosmos3-Nano backbones, our Physis-Lang-enhanced models surpass the leading proprietary Veo 3.1 model.

One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages. Mathematical models were sought as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. At the same time, the approximation of neural networks can reproduce the solution extremely well if fed with a sufficient amount of data. The difference is that an ANN requires big data to build its accurate approximation whereas a typical mathematical model needs just several data points to estimate an empirical constant. Therefore, the common problem that developer meet is the inaccuracy of mathematical models and artificial neural network. An another common challenge is the computational complexity of the mathematical models, or lack of data for a sufficient precision of the Artificial Neural Networks. In the presented paper those problems are addressed using the integration of a mathematical model with an artificial neural network. In the presented analysis, an ANN predicts just a part of the mathematical model and its weights and biases are adjusted based on the output of the mathematical model. The performance of Integrated Mathematical modeling - Artificial Neural Network (IMANN) is compared to a Dense Neural Network (DNN) with the use of the benchmarking functions. The obtained calculation results indicate that such an approach could lead to an increase of precision as well as limiting the data-set required for learning.

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.

Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and topologically simpler, including also Boy surface (real projective plane), using a family of ruled surfaces. We show their usefulness in visualizing the process using commonly available modeling software.

In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and algorithms become more powerful, an intriguing possibility arises - the interplay between human intuition and computer algorithms can lead to discoveries of novel mathematical concepts that would otherwise remain elusive. To realize this perspective, we have developed a massively parallel computer algorithm that discovers an unprecedented number of continued fraction formulas for fundamental mathematical constants. The sheer number of formulas discovered by the algorithm unveils a novel mathematical structure that we call the conservative matrix field. Such matrix fields (1) unify thousands of existing formulas, (2) generate infinitely many new formulas, and most importantly, (3) lead to unexpected relations between different mathematical constants, including multiple integer values of the Riemann zeta function. Conservative matrix fields also enable new mathematical proofs of irrationality. In particular, we can use them to generalize the celebrated proof by Ap\'ery for the irrationality of zeta(3). Utilizing thousands of personal computers worldwide, our computer-supported research strategy demonstrates the power of experimental mathematics, highlighting the prospects of large-scale computational approaches to tackle longstanding open problems and discover unexpected connections across diverse fields of science.

Automated discovery of physical laws from observational data in the real world is a grand challenge in AI. Current methods, relying on symbolic regression or LLMs, are limited to uni-modal data and overlook the rich, visual phenomenological representations of motion that are indispensable to physicists. This "sensory deprivation" severely weakens their ability to interpret the inherent spatio-temporal patterns within dynamic phenomena. To address this gap, we propose VIPER-R1, a multimodal model that performs Visual Induction for Physics-based Equation Reasoning to discover fundamental symbolic formulas. It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process. The model is trained via a curriculum of Motion Structure Induction (MSI), using supervised fine-tuning to interpret kinematic phase portraits and to construct hypotheses guided by a Causal Chain of Thought (C-CoT), followed by Reward-Guided Symbolic Calibration (RGSC) to refine the formula structure with reinforcement learning. During inference, the trained VIPER-R1 acts as an agent: it first posits a high-confidence symbolic ansatz, then proactively invokes an external symbolic regression tool to perform Symbolic Residual Realignment (SR^2). This final step, analogous to a physicist's perturbation analysis, reconciles the theoretical model with empirical data. To support this research, we introduce PhysSymbol, a new 5,000-instance multimodal corpus. Experiments show that VIPER-R1 consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability, enabling more precise discovery of physical laws. Project page: https://jiaaqiliu.github.io/VIPER-R1/

The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential, however, the early MSA formulations (which were widely adopted) only included the terms needed to compute the mean excess chemical potential (or the mean activity coefficient). Other terms for the chemical potential μ_i of individual species i were not included because they sum to 0 in the mean chemical potential. Here, we derive these terms to give a complete MSA formulation of the chemical potential. The result is a simple additive term for μ_i that we show is a qualitative improvement over the previous MSA version. In addition, our derivation shows that the MSA's assumption of global charge neutrality is not strictly necessary, so that the MSA is also valid for systems close to neutrality.

The binding energies of the five bound rotational levels J=0-4 in the highest vibrational level v=14 in the X^1Sigma_g^+ ground electronic state of H_2 were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H_2S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F^1Sigma_g^+ - X^1Sigma_g^+ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The s-wave scattering length of the H + H system is derived from the binding energy of the last bound J=0 level via a direct semi-empirical approach, yielding a value of a_s = 0.2724(5) a_0, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the malpha^4 relativity contribution to a_s was found to be significant. In a similar manner a value for the p-wave scattering volume is determined via the J=1 binding energy yielding a_p = -134.0000(6) a_0^3. The binding energy of the last bound state in H_2, the (v=14, J=4) level, is determined at 0.023(4) cm^{-1}, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed.

Text and formulas constitute the core informational components of many documents. Accurately and efficiently recognizing both is crucial for developing robust and generalizable document parsing systems. Recently, vision-language models (VLMs) have achieved impressive unified recognition of text and formulas. However, they are large-sized and computationally demanding, restricting their usage in many applications. In this paper, we propose UniRec-0.1B, a unified recognition model with only 0.1B parameters. It is capable of performing text and formula recognition at multiple levels, including characters, words, lines, paragraphs, and documents. To implement this task, we first establish UniRec40M, a large-scale dataset comprises 40 million text, formula and their mix samples, enabling the training of a powerful yet lightweight model. Secondly, we identify two challenges when building such a lightweight but unified expert model. They are: structural variability across hierarchies and semantic entanglement between textual and formulaic content. To tackle these, we introduce a hierarchical supervision training that explicitly guides structural comprehension, and a semantic-decoupled tokenizer that separates text and formula representations. Finally, we develop a comprehensive evaluation benchmark covering Chinese and English documents from multiple domains and with multiple levels. Experimental results on this and public benchmarks demonstrate that UniRec-0.1B outperforms both general-purpose VLMs and leading document parsing expert models, while achieving a 2-9times speedup, validating its effectiveness and efficiency. Codebase and Dataset: https://github.com/Topdu/OpenOCR.

We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with DFT calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical accuracy on the scale of milliseconds. FCHL19 is a revision of our previous work [Faber et al. 2018] where the representation is discretized and the individual features are rigorously optimized using Monte Carlo optimization. Combined with a Gaussian kernel function that incorporates elemental screening, chemical accuracy is reached for energy learning on the QM7b and QM9 datasets after training for minutes and hours, respectively. The model also shows good performance for non-bonded interactions in the condensed phase for a set of water clusters with an MAE binding energy error of less than 0.1 kcal/mol/molecule after training on 3,200 samples. For force learning on the MD17 dataset, our optimized model similarly displays state-of-the-art accuracy with a regressor based on Gaussian process regression. When the revised FCHL19 representation is combined with the operator quantum machine learning regressor, forces and energies can be predicted in only a few milliseconds per atom. The model presented herein is fast and lightweight enough for use in general chemistry problems as well as molecular dynamics simulations.

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.

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, an all-round framework is presented which relies on a feedforward neural network, the selection of physically-meaningful features and, when applicable, joint-learning. Next to being faster in terms of training time, this approach is shown to outperform current graph-network models on small datasets. In particular, the vibrational entropy at 305 K of crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint-learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps understanding the underlying physics.

Modern foundational Multimodal Large Language Models (MLLMs) and video world models have advanced significantly in mathematical, common-sense, and visual reasoning, but their grasp of the underlying physics remains underexplored. Existing benchmarks attempting to measure this matter rely on synthetic, Visual Question Answer templates or focus on perceptual video quality that is tangential to measuring how well the video abides by physical laws. To address this fragmentation, we introduce PhysicsMind, a unified benchmark with both real and simulation environments that evaluates law-consistent reasoning and generation over three canonical principles: Center of Mass, Lever Equilibrium, and Newton's First Law. PhysicsMind comprises two main tasks: i) VQA tasks, testing whether models can reason and determine physical quantities and values from images or short videos, and ii) Video Generation(VG) tasks, evaluating if predicted motion trajectories obey the same center-of-mass, torque, and inertial constraints as the ground truth. A broad range of recent models and video generation models is evaluated on PhysicsMind and found to rely on appearance heuristics while often violating basic mechanics. These gaps indicate that current scaling and training are still insufficient for robust physical understanding, underscoring PhysicsMind as a focused testbed for physics-aware multimodal models. Our data will be released upon acceptance.

Large language models can answer scientific questions, yet a correct output does not reveal whether the model represents or uses the governing physics. Here we show that materials science mechanism information in the open-weight google/gemma-4-E4B-it model has three experimentally separable forms: concepts are readable in individual hidden states, constitutive orientation is carried by controlled transformations between states, and selected internal representations causally control engineering answers. We combine matched direct and Jacobian vocabulary readouts, option-free state geometry, a 60-law counterfactual benchmark and causal interventions. In 50 held-out materials descriptions, three independently fitted Jacobian lenses reproduced concept ranks, and target-free word sets from both readouts enabled blinded identification of 9 of 10 mechanism families. A separate 72-prompt benchmark produced mechanism-specific hidden-state neighborhoods, but an exact graph audit showed that this apparent physical organization was equally explained by numerical comparison. We therefore compared otherwise identical prompts in which only the direction of the physical input was reversed, asking whether the resulting hidden-state movement followed the supplied constitutive law. These state transformations ordered direct, physically neutral and inverse laws across 60 frozen relations and correctly oriented 39 of 40 directional laws, whereas lexical controls were near chance. Bidirectional interventions shifted answer probabilities toward or away from the physically appropriate outcome across all 12 matched cases, while counterfactual state patches transferred opposing decision signals across mechanisms and answer formats. Physical relationships were therefore more visible in controlled state changes than in absolute states alone.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

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.

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.

Pre-trained on extensive text and image corpora, current Multi-Modal Large Language Models (MLLM) have shown strong capabilities in general visual reasoning tasks. However, their performance is still lacking in physical domains that require understanding diagrams with complex physical structures and quantitative analysis based on multi-modal information. To address this, we develop a new framework, named Multi-Modal Scientific Reasoning with Physics Perception and Simulation (MAPS) based on an MLLM. MAPS decomposes expert-level multi-modal reasoning task into physical diagram understanding via a Physical Perception Model (PPM) and reasoning with physical knowledge via a simulator. The PPM module is obtained by fine-tuning a visual language model using carefully designed synthetic data with paired physical diagrams and corresponding simulation language descriptions. At the inference stage, MAPS integrates the simulation language description of the input diagram provided by PPM and results obtained through a Chain-of-Simulation process with MLLM to derive the underlying rationale and the final answer. Validated using our collected college-level circuit analysis problems, MAPS significantly improves reasoning accuracy of MLLM and outperforms all existing models. The results confirm MAPS offers a promising direction for enhancing multi-modal scientific reasoning ability of MLLMs. We will release our code, model and dataset used for our experiments upon publishing of this paper.

The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We proved two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is: the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reaction. Physically, this means that the irreversible reactions cannot be included in oriented pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.

This thesis is divided into three parts. The first part deals with cylindric plane partitions. The second with lambda-determinants and the third with commutators in semi-circular systems. For more detailed abstract please see inside. Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of section one is a new bijective proof of Borodin's identity which makes use of Fomin's growth diagram framework for generalized RSK correspondences. The second result is a (q,t)-analog of Borodin's identity which extends previous work by Okada in the reverse plane partition case. The third result is an explicit combinatorial interpretation of the Macdonald weight occurring in the (q,t)-analog using the non-intersecting lattice path model for cylindric plane partitions. Alternating sign matrices were discovered by Robbins and Rumsey whilst studying λ-determinants. In the second part of this thesis we prove a multi-parameter generalization of the λ-determinant, generalizing a recent result by di Francesco. Like the original λ-determinant, our formula exhibits the Laurent phenomenon. Semicircular systems were first introduced by Voiculescu as a part of his study of von Neumann algebras. In the third part of this thesis we study certain commutator subalgebras of the semicircular system. We find a projection matrix with an interesting self-similar structure. Making use of our projection formula we given an alternative, elementary proof that the semicircular system is a factor.

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial-mass planets of all compositions we considered follow a generic functional form that is not a simple power law: log_{10} R_s = k_1 + 1/3 log_{10}(M_s) - k_2 M_s^{k_3} for up to M_p approx 20 M_{oplus}, where M_s and R_s are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form rho = rho_0 + c P^n. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found that: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with sim~5% uncertainty water ice planets with gtrsim 25% water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super Earths'' based on the clear distinction in radii between planets with significant gas envelopes and those without.

Formula recognition presents significant challenges due to the complicated structure and varied notation of mathematical expressions. Despite continuous advancements in formula recognition models, the evaluation metrics employed by these models, such as BLEU and Edit Distance, still exhibit notable limitations. They overlook the fact that the same formula has diverse representations and is highly sensitive to the distribution of training data, thereby causing the unfairness in formula recognition evaluation. To this end, we propose a Character Detection Matching (CDM) metric, ensuring the evaluation objectivity by designing a image-level rather than LaTex-level metric score. Specifically, CDM renders both the model-predicted LaTeX and the ground-truth LaTeX formulas into image-formatted formulas, then employs visual feature extraction and localization techniques for precise character-level matching, incorporating spatial position information. Such a spatially-aware and character-matching method offers a more accurate and equitable evaluation compared with previous BLEU and Edit Distance metrics that rely solely on text-based character matching. Experimentally, we evaluated various formula recognition models using CDM, BLEU, and ExpRate metrics. Their results demonstrate that the CDM aligns more closely with human evaluation standards and provides a fairer comparison across different models by eliminating discrepancies caused by diverse formula representations.

This work aims to develop a method based on a structurally reliable ice model and a statistically and physico-chemically robust approach for BE distribution inference, with the aim to be applicable to various relevant interstellar species. A multiscale computational approach is presented, with a Molecular Dynamics (MD) Heat & Quench protocol for the amorphous water ice model, and an ONIOM(B3LYP-D3(BJ)/6-311+G**:GFN2-xtb) scheme for the BE inference, with a prime emphasis onto the BE/real system size convergence. The sampling of the binding configurations is twofold, exploring both regularly spaced binding sites, as well as various adsorbate-to-substrate orientations on each locally distinct site. This second source of BE diversity accounts for the local roughness of the potential energy landscape of the substrate. Three different adsorbate test cases are considered, i.e. NH3, CO and CH4, owing to their significance in dust icy mantles, and their distinct binding behavior with water ices. The BE distributions for NH3, CO and CH4 have been inferred, with converged statistics. The distribution for NH3 is better represented by a double Gaussian component profile. Three starting adsorbate orientations per site are required to reach convergence for both Gaussian components of NH3, while 2 orientations are sufficient for CO, and one unique for CH4 (symmetric). Further geometrical and molecular surrounding insights have been provided. These results encompass previously reported results.

Machine learning weather prediction (MLWP) models have achieved impressive forecasting performance at a small fraction of the computational costs required for traditional physics-based methods. However, they are primarily (1) data-driven and (2) evaluated using pixel-wide error metrics (e.g., RMSE), so there are no guarantees that their forecasts are consistent with known physical laws. We introduce PhysMetrics.Weather, an evaluation framework that assesses the physical realism of MLWP models across three types of metrics: conservation, spectral, and dynamical. By quantifying physical realism, this tool guides the development of physics-informed architectures and helps evaluate whether MLWP models are reliable for operational use. Our framework is available on Github at https://github.com/Emmakast/PhysMetrics.Weather.

Based on the standard Gaisser's formula, a modified parametrization for the sea-level cosmic-ray muon flux is introduced. The modification is verified against experimental results. The average vertical cosmic-ray muon intensity as a function of depth of standard rock is simulated using the modified formula as input to the MUSIC code. The calculated muon intensities is consistent with the experimental measurements.

The Gauge-Including Projector Augmented Wave (GIPAW) method, within the Density Functional Theory (DFT) Generalized Gradient Approximation (GGA) framework, is applied to compute solid state NMR parameters for ^{27}Al in the α, θ, and κ aluminium oxide phases and their gibbsite and boehmite precursors. The results for well-established crystalline phases compare very well with available experimental data and provide confidence in the accuracy of the method. For γ-alumina, four structural models proposed in the literature are discussed in terms of their ability to reproduce the experimental spectra also reported in the literature. Among the considered models, the Fd3m structure proposed by Paglia {\it et al.} [Phys. Rev. B {\bf 71}, 224115 (2005)] shows the best agreement. We attempt to link the theoretical NMR parameters to the local geometry. Chemical shifts depend on coordination number but no further correlation is found with geometrical parameters. Instead our calculations reveal that, within a given coordination number, a linear correlation exists between chemical shifts and Born effective charges.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

This article establishes a complete approximate axiomatization for the real-closed field R expanded with all differentially-defined functions, including special functions such as sin(x), cos(x), e^x, dots. Every true sentence is provable up to some numerical approximation, and the truth of such approximations converge under mild conditions. Such an axiomatization is a fragment of the axiomatization for differential dynamic logic, and is therefore a finite extension of the axiomatization of real-closed fields. Furthermore, the numerical approximations approximate formulas containing special function symbols by FOL_{R} formulas, improving upon earlier decidability results only concerning closed sentences.

This paper gives three formulas for the pseudoinverse of a matrix product A = CR. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse A^+_r may be very useful when A is a very large matrix. 1. A^+ = R^+C^+ when A = CR and C has independent columns and R has independent rows. 2. A^+ = (C^+CR)^+(CRR^+)^+ is always correct. 3. A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+ only when rank(P^TA) = rank(AQ) = rank(A) with A = CR.

Recent progress in large language models (LLMs) has moved the frontier from puzzle-solving to science-grade reasoning-the kind needed to tackle problems whose answers must stand against nature, not merely fit a rubric. Physics is the sharpest test of this shift, which binds symbols to reality in a fundamental way, serving as the cornerstone of most modern technologies. In this work, we manage to advance physics research by developing large language models with exceptional physics reasoning capabilities, especially excel at solving Olympiad-level physics problems. We introduce P1, a family of open-source physics reasoning models trained entirely through reinforcement learning (RL). Among them, P1-235B-A22B is the first open-source model with Gold-medal performance at the latest International Physics Olympiad (IPhO 2025), and wins 12 gold medals out of 13 international/regional physics competitions in 2024/2025. P1-30B-A3B also surpasses almost all other open-source models on IPhO 2025, getting a silver medal. Further equipped with an agentic framework PhysicsMinions, P1-235B-A22B+PhysicsMinions achieves overall No.1 on IPhO 2025, and obtains the highest average score over the 13 physics competitions. Besides physics, P1 models also present great performance on other reasoning tasks like math and coding, showing the great generalibility of P1 series.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in diverse reasoning tasks, yet their application to complex physics reasoning remains underexplored. Physics reasoning presents unique challenges, requiring grounding in physical conditions and the interpretation of multimodal information. Current physics benchmarks are limited, often focusing on text-only inputs or solely on problem-solving, thereby overlooking the critical intermediate steps of variable identification and process formulation. To address these limitations, we introduce PhysicsArena, the first multimodal physics reasoning benchmark designed to holistically evaluate MLLMs across three critical dimensions: variable identification, physical process formulation, and solution derivation. PhysicsArena aims to provide a comprehensive platform for assessing and advancing the multimodal physics reasoning abilities of MLLMs.

The ability to precisely derive mathematical objects is a core requirement for downstream STEM applications, including mathematics, physics, and chemistry, where reasoning must culminate in formally structured expressions. Yet, current LM evaluations of mathematical and scientific reasoning rely heavily on simplified answer formats such as numerical values or multiple choice options due to the convenience of automated assessment. In this paper we provide three contributions for improving reasoning over mathematical objects: (i) we build and release training data and benchmarks for deriving mathematical objects, the Principia suite; (ii) we provide training recipes with strong LLM-judges and verifiers, where we show that on-policy judge training boosts performance; (iii) we show how on-policy training can also be used to scale test-time compute via aggregation. We find that strong LMs such as Qwen3-235B and o3 struggle on Principia, while our training recipes can bring significant improvements over different LLM backbones, while simultaneously improving results on existing numerical and MCQA tasks, demonstrating cross-format generalization of reasoning abilities.

In this work, we present web scraping techniques to extract in- formation from patent tables, clean and structure them for future use in predictive machine learning models to develop new glasses. We extracted compositions and three properties relevant to the development of new glasses and structured them into a database to be used together with information from other available datasets. We also analyzed the consistency of the information obtained and what it adds to the existing databases. The extracted liquidus temperatures comprise 5,696 compositions; the second subset includes 4,298 refractive indexes and, finally, 1,771 compositions with Abbe numbers. The extraction performed here increases the available information by approximately 10.4% for liquidus temperature, 6.6% for refractive index, and 4.9% for Abbe number. The impact extends beyond quantity: the newly extracted data introduce compositions with property values that are more diverse than those in existing databases, thereby expanding the accessible compositional and property space for glass modeling applications. We emphasize that the compositions of the new database contain relatively more titanium, magnesium, zirconium, niobium, iron, tin, and yttrium oxides than those of the existing bases.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Many chemical concepts can be well defined in the context of quantum chemical theories. Examples are the electronegativity scale of Mulliken and Jaffe and the hard and soft acids and bases concept of Pearson. The sound theoretical basis allows for a systematic definition of such concepts. However, while they are often used to describe and compare chemical processes in terms of reactivity, their predictive power remains unclear. In this work, we elaborate on the predictive potential of chemical reactivity concepts, which can be crucial for autonomous reaction exploration protocols to guide them by first-principles heuristics that expoit these concepts.

Understanding physical phenomena is a key competence that enables humans and animals to act and interact under uncertain perception in previously unseen environments containing novel object and their configurations. Developmental psychology has shown that such skills are acquired by infants from observations at a very early stage. In this paper, we contrast a more traditional approach of taking a model-based route with explicit 3D representations and physical simulation by an end-to-end approach that directly predicts stability and related quantities from appearance. We ask the question if and to what extent and quality such a skill can directly be acquired in a data-driven way bypassing the need for an explicit simulation. We present a learning-based approach based on simulated data that predicts stability of towers comprised of wooden blocks under different conditions and quantities related to the potential fall of the towers. The evaluation is carried out on synthetic data and compared to human judgments on the same stimuli.

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.

Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly less attention. Existing benchmarks often fall short in evaluating LLMs' abilities on the breadth and depth of undergraduate-level physics, underscoring the need for a comprehensive evaluation. To fill this gap, we introduce UGPhysics, a large-scale and comprehensive benchmark specifically designed to evaluate UnderGraduate-level Physics (UGPhysics) reasoning with LLMs. UGPhysics includes 5,520 undergraduate-level physics problems in both English and Chinese, covering 13 subjects with seven different answer types and four distinct physics reasoning skills, all rigorously screened for data leakage. Additionally, we develop a Model-Assistant Rule-based Judgment (MARJ) pipeline specifically tailored for assessing answer correctness of physics problems, ensuring accurate evaluation. Our evaluation of 31 leading LLMs shows that the highest overall accuracy, 49.8% (achieved by OpenAI-o1-mini), emphasizes the necessity for models with stronger physics reasoning skills, beyond math abilities. We hope UGPhysics, along with MARJ, will drive future advancements in AI for physics reasoning.

This paper studies the problem of solving complex chemistry problems with large language models (LLMs). Despite the extensive general knowledge in LLMs (such as GPT-4), they struggle with chemistry reasoning that requires faithful grounded reasoning with diverse chemical knowledge and an integrative understanding of chemical interactions. We propose InstructChem, a new structured reasoning approach that substantially boosts the LLMs' chemical reasoning capabilities. InstructChem explicitly decomposes the reasoning into three critical phrases, including chemical formulae generation by LLMs that offers the basis for subsequent grounded reasoning, step-by-step reasoning that makes multi-step derivations with the identified formulae for a preliminary answer, and iterative review-and-refinement that steers LLMs to progressively revise the previous phases for increasing confidence, leading to the final high-confidence answer. We conduct extensive experiments on four different chemistry challenges, including quantum chemistry, quantum mechanics, physical chemistry, and chemistry kinetics. Our approach significantly enhances GPT-4 on chemistry reasoning, yielding an 8% average absolute improvement and a 30% peak improvement. We further use the generated reasoning by GPT-4 to fine-tune smaller LMs (e.g., Vicuna) and observe strong improvement of the smaller LMs. This validates our approach and enables LLMs to generate high-quality reasoning.

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.

Accurate mechanical properties (or materials) Young's modulus (E), Poisson's ratio (ν) and density (ρ) are essential for reliable physics simulation of digital worlds, but most 3D assets lack this information. We propose AdaVoMP, a method for predicting accurate dense spatially-varying (E, ν, ρ) for input 3D objects across representations, improving the resolution, accuracy, and memory efficiency over the state-of-the-art. The foundation of our technique is a sparse and adaptive voxel structure SAV that efficiently represents both the input 3D shape and the material field output. We replace the fixed-voxel model of the most accurate prior method, VoMP, with a novel sparse transformer encoder-decoder model that learns to generate a unique SAV autoregressively for every input shape to represent its materials, achieving a resolution 16^3times higher than prior art. Experiments show that AdaVoMP estimates more accurate volumetric properties, even with lesser test-time compute than all prior art. This allows us to convert high-resolution complex 3D objects into simulation-ready assets, resulting in realistic deformable simulations.

Estimating physical properties for visual data is a crucial task in computer vision, graphics, and robotics, underpinning applications such as augmented reality, physical simulation, and robotic grasping. However, this area remains under-explored due to the inherent ambiguities in physical property estimation. To address these challenges, we introduce GaussianProperty, a training-free framework that assigns physical properties of materials to 3D Gaussians. Specifically, we integrate the segmentation capability of SAM with the recognition capability of GPT-4V(ision) to formulate a global-local physical property reasoning module for 2D images. Then we project the physical properties from multi-view 2D images to 3D Gaussians using a voting strategy. We demonstrate that 3D Gaussians with physical property annotations enable applications in physics-based dynamic simulation and robotic grasping. For physics-based dynamic simulation, we leverage the Material Point Method (MPM) for realistic dynamic simulation. For robot grasping, we develop a grasping force prediction strategy that estimates a safe force range required for object grasping based on the estimated physical properties. Extensive experiments on material segmentation, physics-based dynamic simulation, and robotic grasping validate the effectiveness of our proposed method, highlighting its crucial role in understanding physical properties from visual data. Online demo, code, more cases and annotated datasets are available on https://Gaussian-Property.github.io{this https URL}.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

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.

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.

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.

This study aims to improve the accuracy of weather predictions by discovering spatial correlations between Earth observations and atmospheric states. Existing numerical weather prediction (NWP) systems predict future atmospheric states at fixed locations, which are called NWP grid points, by analyzing previous atmospheric states and newly acquired Earth observations. However, the shifting locations of observations and the surrounding meteorological context induce complex, dynamic spatial correlations that are difficult for traditional NWP systems to capture, since they rely on strict statistical and physical formulations. To handle complicated spatial correlations, which change dynamically, we employ a spatiotemporal graph neural networks (STGNNs) with structure learning. However, structure learning has an inherent limitation that this can cause structural information loss and over-smoothing problem by generating excessive edges. To solve this problem, we regulate edge sampling by adaptively determining node degrees and considering the spatial distances between NWP grid points and observations. We validated the effectiveness of the proposed method (CloudNine-v2) using real-world atmospheric state and observation data from East Asia, achieving up to 15\% reductions in RMSE over existing STGNN models. Even in areas with high atmospheric variability, CloudNine-v2 consistently outperformed baselines with and without structure learning.

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wavefunction. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

Existing benchmarks fail to capture a crucial aspect of intelligence: physical reasoning, the integrated ability to combine domain knowledge, symbolic reasoning, and understanding of real-world constraints. To address this gap, we introduce PhyX: the first large-scale benchmark designed to assess models capacity for physics-grounded reasoning in visual scenarios. PhyX includes 3K meticulously curated multimodal questions spanning 6 reasoning types across 25 sub-domains and 6 core physics domains: thermodynamics, electromagnetism, mechanics, modern physics, optics, and wave\&acoustics. In our comprehensive evaluation, even state-of-the-art models struggle significantly with physical reasoning. GPT-4o, Claude3.7-Sonnet, and GPT-o4-mini achieve only 32.5\%, 42.2\%, and 45.8\% accuracy respectively-performance gaps exceeding 29\% compared to human experts. Our analysis exposes critical limitations in current models: over-reliance on memorized disciplinary knowledge, excessive dependence on mathematical formulations, and surface-level visual pattern matching rather than genuine physical understanding. We provide in-depth analysis through fine-grained statistics, detailed case studies, and multiple evaluation paradigms to thoroughly examine physical reasoning capabilities. To ensure reproducibility, we implement a compatible evaluation protocol based on widely-used toolkits such as VLMEvalKit, enabling one-click evaluation.

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question-answer (QA) pairs, a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question-answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5-10 percentage points across model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data. Code available at: https://sim2reason.github.io/.

We carried out numerical simulations of propagation of spin waves (magnons in quantum language) in a yttrium-iron garnet film. The numerical model is based on an original formalism. We demonstrated that a potential barrier for magnons, created by an Oersted field of a dc current flowing through a wire sitting on top of the film, is able to act as an electrically controlled partly transparent mirror for the magnons. We found that the mirror transparency can be set to 50% by properly adjusting the current strength, thus creating a semi-transparent mirror. A strong Hong-Ou-Mandel Effect for single magnons is expected in this configuration. The effect must be seen as two single magnons, launched simultaneously into the film from two transducers located from the opposite sides of the mirror, creating a two-microwave-photon state at the output port of one of the transducers. The probability of seeing those two-photon states at the output port of either transducer must be the same for both transducers.

Many-body perturbation theory is a powerful framework to calculate spectroscopic quantities, as well as the total energy. However, the field suffers from the fact that different flavors of approximations lead to a wide range of results. We present several in principle exact expansions and discuss how to use them consistently. We concentrate on the first two orders in the respective screened Coulomb interaction. Of special interest is a consistent expansion around the Kohn-Sham system. We illustrate the performance of the various choices using the symmetric Hubbard dimer over a wide range of correlation strength. In particular, the expansion based on exact Kohn-Sham ingredients stands out as a promising route towards good energies and good spectra.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

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.

Machine-learned interatomic potentials trained across the periodic table have made atomistic simulation broadly accessible, and specializing them to a single compound class is widely expected to improve accuracy. Yet examples remain scarce, and fewer still surpass universal models in speed or reach a higher level of electronic-structure theory. Here we present a potential that is universal within the class of water-free solid-state hydrogen-bond network mediated proton conductors rather than across chemistry and a database of 4.4 million first-principles configurations spanning 55 materials. It surpasses leading general-purpose potentials across this domain, recovering measured activation energies and the ordering of anion rotational dynamics that those models miss; agreement on static structure does not imply agreement on transport. Accuracy falls for compositions far from the training set but stays competitive for close structural relatives, and a higher level of electronic-structure theory is reached with a few hundred additional configurations per material. We further introduce a compact variant carrying a fifth of the parameters, faster still and yet more accurate than every general-purpose model tested. It sustains more than a quarter of a million atoms on a single graphics processor, placing grain boundaries and the transition into the highly conducting phase within reach, and making a quantum treatment of the protons affordable. Reference accuracy and accessible system size thus become largely independent, offering a template for other compound classes.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

Driven by the growing capacity and training scale, Text-to-Video (T2V) generation models have recently achieved substantial progress in video quality, length, and instruction-following capability. However, whether these models can understand physics and generate physically plausible videos remains a question. While Vision-Language Models (VLMs) have been widely used as general-purpose evaluators in various applications, they struggle to identify the physically impossible content from generated videos. To investigate this issue, we construct a PID (Physical Implausibility Detection) dataset, which consists of a test split of 500 manually annotated videos and a train split of 2,588 paired videos, where each implausible video is generated by carefully rewriting the caption of its corresponding real-world video to induce T2V models producing physically implausible content. With the constructed dataset, we introduce a lightweight fine-tuning approach, enabling VLMs to not only detect physically implausible events but also generate textual explanations on the violated physical principles. Taking the fine-tuned VLM as a physical plausibility detector and explainer, namely PhyDetEx, we benchmark a series of state-of-the-art T2V models to assess their adherence to physical laws. Our findings show that although recent T2V models have made notable progress toward generating physically plausible content, understanding and adhering to physical laws remains a challenging issue, especially for open-source models. Our dataset, training code, and checkpoints are available at https://github.com/Zeqing-Wang/PhyDetEx{https://github.com/Zeqing-Wang/PhyDetEx}.

Identifying subtle technical errors within complex scientific and technical documents, especially those requiring multimodal interpretation (e.g., formulas in images), presents a significant hurdle for Large Language Models (LLMs) whose inherent error-correction tendencies can mask inaccuracies. This exploratory proof-of-concept (PoC) study investigates structured LLM context conditioning, informed by Persistent Workflow Prompting (PWP) principles, as a methodological strategy to modulate this LLM behavior at inference time. The approach is designed to enhance the reliability of readily available, general-purpose LLMs (specifically Gemini 2.5 Pro and ChatGPT Plus o3) for precise validation tasks, crucially relying only on their standard chat interfaces without API access or model modifications. To explore this methodology, we focused on validating chemical formulas within a single, complex test paper with known textual and image-based errors. Several prompting strategies were evaluated: while basic prompts proved unreliable, an approach adapting PWP structures to rigorously condition the LLM's analytical mindset appeared to improve textual error identification with both models. Notably, this method also guided Gemini 2.5 Pro to repeatedly identify a subtle image-based formula error previously overlooked during manual review, a task where ChatGPT Plus o3 failed in our tests. These preliminary findings highlight specific LLM operational modes that impede detail-oriented validation and suggest that PWP-informed context conditioning offers a promising and highly accessible technique for developing more robust LLM-driven analytical workflows, particularly for tasks requiring meticulous error detection in scientific and technical documents. Extensive validation beyond this limited PoC is necessary to ascertain broader applicability.

In this paper an alternative way of conducting the physics laboratory exercise for determining the adiabatic index of air using the Clement -- Desormes method is proposed. The process of isochoric cooling of air has been studied in terms of the dependence of pressure on time, and hence temperature on time, since it is proportional to pressure at a constant volume and mass of air. A theoretical model of the considered process was also made. The experimental results were processed statistically. The coefficient of determination R^2 and the F-test statistic were calculated and their values indicate a very good agreement between theory and experiment. The analysis of the residuals, however, implies that the model could be further improved through the inclusion of higher order terms.

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.

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into the training of the neural network (NN) based on such a data set. In PINNs, the NN acts as the solution approximator for the PDE while the PDE acts as the prior knowledge to guide the NN training, leading to the desired generalization performance of the NN when facing the limited availability of training data. However, training PINNs is a non-trivial task largely due to the complexity of the loss composed of both NN and physical law parts. In this work, we propose a new PINN training framework based on the multi-task optimization (MTO) paradigm. Under this framework, multiple auxiliary tasks are created and solved together with the given (main) task, where the useful knowledge from solving one task is transferred in an adaptive mode to assist in solving some other tasks, aiming to uplift the performance of solving the main task. We implement the proposed framework and apply it to train the PINN for addressing the traffic density prediction problem. Experimental results demonstrate that our proposed training framework leads to significant performance improvement in comparison to the traditional way of training the PINN.

Multimodal large language models (MLLMs) are increasingly envisioned as core components of scientific and engineering agents, yet their ability to interpret physical fields remains poorly understood. Existing physics benchmarks largely emphasize textbook problem solving or intuitive physical reasoning, leaving open whether MLLMs can infer physically meaningful information from continuous field observations. We introduce PhysFieldBench, a benchmark comprising 24 tasks and 1,160 evaluation examples across controlled equation fields, simulated physical fields, and observed physical fields. The tasks assess three forms of inference: identifying physical mechanisms, comparing latent control variables, and predicting outcome properties. Across representative open-source and proprietary MLLMs, zero-shot performance is low: the best model achieves a chance-normalized score of 29.3, while several open-source models remain near chance. In contrast, a task-specific supervised vision transformer performs substantially better, demonstrating that the inputs contain learnable physical information. To diagnose these failures, a structured self-explanation analysis attributes most errors to missed visual patterns and incorrect visual-to-physical mappings. Further, to explore whether post-training can improve physical inference and generalize to unseen tasks, we compare supervised fine-tuning with final answers or chain-of-thought supervision and reinforcement learning. Final-answer supervision performs best overall but transfers less effectively, whereas reinforcement learning after chain-of-thought supervision achieves the best generalization. Together, these findings highlight the need to improve visual-to-physical grounding and cross-task generalization for MLLMs to reliably interpret physical fields in scientific and engineering workflows.

The specialized language and complex concepts in physics pose significant challenges for information extraction through Natural Language Processing (NLP). Central to effective NLP applications is the text embedding model, which converts text into dense vector representations for efficient information retrieval and semantic analysis. In this work, we introduce PhysBERT, the first physics-specific text embedding model. Pre-trained on a curated corpus of 1.2 million arXiv physics papers and fine-tuned with supervised data, PhysBERT outperforms leading general-purpose models on physics-specific tasks including the effectiveness in fine-tuning for specific physics subdomains.

The accuracy of any machine learning potential can only be as good as the data used in the fitting process. The most efficient model therefore selects the training data that will yield the highest accuracy compared to the cost of obtaining the training data. We investigate the convergence of prediction errors of quantum machine learning models for organic molecules trained on energy and force labels, two common data types in molecular simulations. When training and predicting on different geometries corresponding to the same single molecule, we find that the inclusion of atomic forces in the training data increases the accuracy of the predicted energies and forces 7-fold, compared to models trained on energy only. Surprisingly, for models trained on sets of organic molecules of varying size and composition in non-equilibrium conformations, inclusion of forces in the training does not improve the predicted energies of unseen molecules in new conformations. Predicted forces, however, also improve about 7-fold. For the systems studied, we find that force labels and energy labels contribute equally per label to the convergence of the prediction errors. Choosing to include derivatives such as atomic forces in the training set or not should thus depend on, not only on the computational cost of acquiring the force labels for training, but also on the application domain, the property of interest, and the desirable size of the machine learning model. Based on our observations we describe key considerations for the creation of datasets for potential energy surfaces of molecules which maximize the efficiency of the resulting machine learning models.

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.

Autoformalization, which translates natural language mathematics into formal statements to enable machine reasoning, faces fundamental challenges in the wild due to the multimodal nature of the physical world, where physics requires inferring hidden constraints (e.g., mass or energy) from visual elements. To address this, we propose MMFormalizer, which extends autoformalization beyond text by integrating adaptive grounding with entities from real-world mathematical and physical domains. MMFormalizer recursively constructs formal propositions from perceptually grounded primitives through recursive grounding and axiom composition, with adaptive recursive termination ensuring that every abstraction is supported by visual evidence and anchored in dimensional or axiomatic grounding. We evaluate MMFormalizer on a new benchmark, PhyX-AF, comprising 115 curated samples from MathVerse, PhyX, Synthetic Geometry, and Analytic Geometry, covering diverse multimodal autoformalization tasks. Results show that frontier models such as GPT-5 and Gemini-3-Pro achieve the highest compile and semantic accuracy, with GPT-5 excelling in physical reasoning, while geometry remains the most challenging domain. Overall, MMFormalizer provides a scalable framework for unified multimodal autoformalization, bridging perception and formal reasoning. To the best of our knowledge, this is the first multimodal autoformalization method capable of handling classical mechanics (derived from the Hamiltonian), as well as relativity, quantum mechanics, and thermodynamics. More details are available on our project page: MMFormalizer.github.io

Tracing the water snowline in low-mass young stellar objects (YSOs) is important because dust grain growth is promoted and the chemical composition varies at the water snowline, which influences planet formation and its properties. In protostellar envelopes, the water snowline can be estimated as a function of luminosity using a relation derived from radiative transfer models, and these predictions are consistent with observations. However, accurately estimating the water snowline in protoplanetary disks requires new relations that account for the disk structure. We present the relations between luminosity and water snowline using the dust continuum radiative transfer models with various density structures. We adopt two-dimensional density structures for an envelope-only model (Model E), an envelope+disk+cavity model (Model E+D), and a protoplanetary disk model (Model PPD). The relations between the water snowline, where T_dust = 100 K, and the total luminosity, ranging 0.1-1,000 solar luminosity, are well fitted by a power-law relation, R_snow=a * (L/L_solar)^p au. The factor a decreases with increasing disk density, while the power index p has values around 0.5 in all models. As the disk becomes denser, the water snowline forms at smaller radii even at the same luminosity, since dense dust hinders photon propagation. We also explore the effect of viscous heating on the water snowline. In Model PPD with viscous heating, the water snowline shifts outward by a few au up to 15 au, increasing the factor a and decreasing the power index p. In Model E+D with lower disk mass, the effect of viscous heating is negligible, indicating that the disk mass controls the effect. The discrepancy between our models and direct observations provides insights into the recent outburst event and the presence of a disk structure in low-mass YSOs.

Machine-learned exchange--correlation (XC) functionals offer a route to improve Kohn--Sham density-functional theory without incurring the cost of explicitly correlated electronic-structure methods. Their use in production simulation codes, however, requires a well-defined mapping between the learned model and the host-code density representation. We formulate and implement a Skala-1.1 interface in CP2K through the external GauXC library. CP2K supplies the geometry, Gaussian basis, spin-resolved atomic-orbital density matrix, and communicator, while GauXC evaluates the XC energy, atomic-orbital potential matrix, and available nuclear derivatives. The interface accepts both all-electron and valence-only density matrices. The latter may arise from separable dual-space pseudopotentials or molecular effective-core potentials. Implementation errors are isolated from functional differences by comparing the Perdew--Burke--Ernzerhof (PBE) functional evaluated through GauXC with native CP2K PBE. The resulting interface gives consistent energies, forces validated against finite-difference total-energy checks, and force-based molecular-virial diagnostics for representative molecular cases. The dietGMTKN55 benchmark suite is evaluated with an all-electron Gaussian augmented plane-wave treatment for elements up to bromine and def2 effective-core potentials for the heavier elements. The resulting aggregate mean absolute deviation of 1.255 kcal/mol is within 0.020 kcal/mol of the corresponding Skala reference value of 1.235 kcal/mol. This work establishes a validated molecular implementation of Skala in CP2K through GauXC.

Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline materials have internal symmetry. However, this is often inadequately addressed by existing generative models, making the consistent generation of stable and symmetrically valid crystal structures a significant challenge. We introduce WyFormer, a generative model that directly tackles this by formally conditioning on space group symmetry. It achieves this by using Wyckoff positions as the basis for an elegant, compressed, and discrete structure representation. To model the distribution, we develop a permutation-invariant autoregressive model based on the Transformer encoder and an absence of positional encoding. Extensive experimentation demonstrates WyFormer's compelling combination of attributes: it achieves best-in-class symmetry-conditioned generation, incorporates a physics-motivated inductive bias, produces structures with competitive stability, predicts material properties with competitive accuracy even without atomic coordinates, and exhibits unparalleled inference speed.

We describe the first-principles design and subsequent synthesis of a new material with the specific functionalities required for a solid-state-based search for the permanent electric dipole moment of the electron. We show computationally that perovskite-structure europium barium titanate should exhibit the required large and pressure-dependent ferroelectric polarization, local magnetic moments, and absence of magnetic ordering even at liquid helium temperature. Subsequent synthesis and characterization of Eu_{0.5}Ba_{0.5}TiO_3 ceramics confirm the predicted desirable properties.

Structure-property relationships are foundational to biology, chemistry and materials science, where function, reactivity and physical response emerge from spatial, chemical and periodic organization. Mechanistically explaining these relationships requires interpreting structural evidence through scientific principles and physical constraints, from stereochemistry and bonding to symmetry, energetics and periodic order. However, applying artificial intelligence to this process presents a joint challenge of representation and reasoning: models must preserve domain-native structural information while showing how specific evidence supports predictions under these constraints. Here we introduce SciReasoner, a multimodal scientific foundation model for native structural reasoning across proteins, small molecules and inorganic crystals. SciReasoner discretizes coordinates, topologies and periodic connectivities into a unified structure-aware vocabulary, treating structural tokens as addressable evidence units during reasoning. In homology-controlled Gene Ontology prediction, SciReasoner improves Cellular Component annotation for low-homology and orphan-like proteins, increasing F_{max} from 0.42 to 0.55. In chemistry, it raises single-step retrosynthesis accuracy from 0.63 to 0.72 while generating fragment-level disconnection and precursor-verification traces. In materials science, its representations separate elemental and compound phases and resolve high- and low-band-gap regimes. Across 86 benchmarks, SciReasoner achieves state-of-the-art performance on 67 tasks. Double-blind expert evaluation rates its reasoning traces as preferred or at least comparable to those of a frontier large language model in 98% of cases. By making structure an inspectable substrate for reasoning under scientific constraints, SciReasoner connects accurate prediction with interpretable scientific inference.