Daily Papers

We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve, particularly conservation laws whose physically relevant solutions contain shocks and discontinuities. FV methods are widely used for their mathematical properties: convergence to entropy solutions, flow conservation, or total variation diminishing, but often lack accuracy and flexibility in complex settings. Neural Finite Volume addresses these limitations by learning update rules over extended spatial and temporal stencils while preserving conservation structure. It supports both supervised training on solution data (NFV) and unsupervised training via weak-form residual loss (UNFV). Applied to first-order conservation laws, (U)NFV achieves up to 10x lower error than Godunov's method, outperforms ENO/WENO, and rivals discontinuous Galerkin solvers with far less complexity. On traffic modeling problems, both from PDEs and from experimental highway data, (U)NFV captures nonlinear wave dynamics with significantly higher fidelity and scalability than traditional FV approaches.

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

Recent video diffusion models can synthesize visually compelling clips, yet often violate basic physical laws-objects float, accelerations drift, and collisions behave inconsistently-revealing a persistent gap between visual realism and physical realism. We propose NewtonRewards, the first physics-grounded post-training framework for video generation based on verifiable rewards. Instead of relying on human or VLM feedback, NewtonRewards extracts measurable proxies from generated videos using frozen utility models: optical flow serves as a proxy for velocity, while high-level appearance features serve as a proxy for mass. These proxies enable explicit enforcement of Newtonian structure through two complementary rewards: a Newtonian kinematic constraint enforcing constant-acceleration dynamics, and a mass conservation reward preventing trivial, degenerate solutions. We evaluate NewtonRewards on five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, and ramp sliding down/up) using our newly constructed large-scale benchmark, NewtonBench-60K. Across all primitives in visual and physics metrics, NewtonRewards consistently improves physical plausibility, motion smoothness, and temporal coherence over prior post-training methods. It further maintains strong performance under out-of-distribution shifts in height, speed, and friction. Our results show that physics-grounded verifiable rewards offer a scalable path toward physics-aware video generation.

Many theoretical results in deep learning can be traced to symmetry or equivariance of neural networks under parameter transformations. However, existing analyses are typically problem-specific and focus on first-order consequences such as conservation laws, while the implications for second-order structure remain less understood. We develop a general equivariance toolbox that yields coupled first- and second-order constraints on learning dynamics. The framework extends classical Noether-type analyses in three directions: from gradient constraints to Hessian constraints, from symmetry to general equivariance, and from continuous to discrete transformations. At the first order, our framework unifies conservation laws and implicit-bias relations as special cases of a single identity. At the second order, it provides structural predictions about curvature: which directions are flat or sharp, how the gradient aligns with Hessian eigenspaces, and how the loss landscape geometry reflects the underlying transformation structure. We illustrate the framework through several applications, recovering known results while also deriving new characterizations that connect transformation structure to modern empirical observations about optimization geometry.

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

As opposed to scaling-up protein language models (PLMs), we seek improving performance via protein-specific optimization. Although the proportionality between the language model size and the richness of its learned representations is validated, we prioritize accessibility and pursue a path of data-efficient, cost-reduced, and knowledge-guided optimization. Through over twenty experiments ranging from masking, architecture, and pre-training data, we derive insights from protein-specific experimentation into building a model that interprets the language of life, optimally. We present Ankh, the first general-purpose PLM trained on Google's TPU-v4 surpassing the state-of-the-art performance with fewer parameters (<10% for pre-training, <7% for inference, and <30% for the embedding dimension). We provide a representative range of structure and function benchmarks where Ankh excels. We further provide a protein variant generation analysis on High-N and One-N input data scales where Ankh succeeds in learning protein evolutionary conservation-mutation trends and introducing functional diversity while retaining key structural-functional characteristics. We dedicate our work to promoting accessibility to research innovation via attainable resources.

The development of effective explainability tools for Transformers is a crucial pursuit in deep learning research. One of the most promising approaches in this domain is Layer-wise Relevance Propagation (LRP), which propagates relevance scores backward through the network to the input space by redistributing activation values based on predefined rules. However, existing LRP-based methods for Transformer explainability entirely overlook a critical component of the Transformer architecture: its positional encoding (PE), resulting in violation of the conservation property, and the loss of an important and unique type of relevance, which is also associated with structural and positional features. To address this limitation, we reformulate the input space for Transformer explainability as a set of position-token pairs. This allows us to propose specialized theoretically-grounded LRP rules designed to propagate attributions across various positional encoding methods, including Rotary, Learnable, and Absolute PE. Extensive experiments with both fine-tuned classifiers and zero-shot foundation models, such as LLaMA 3, demonstrate that our method significantly outperforms the state-of-the-art in both vision and NLP explainability tasks. Our code is publicly available.

The cultural heritage buildings (CHB), which are part of mankind's history and identity, are in constant danger of damage or in extreme situations total destruction. That being said, it's of utmost importance to preserve them by identifying the existent, or presumptive, defects using novel methods so that renovation processes can be done in a timely manner and with higher accuracy. The main goal of this research is to use new deep learning (DL) methods in the process of preserving CHBs (situated in Iran); a goal that has been neglected especially in developing countries such as Iran, as these countries still preserve their CHBs using manual, and even archaic, methods that need direct human supervision. Having proven their effectiveness and performance when it comes to processing images, the convolutional neural networks (CNN) are a staple in computer vision (CV) literacy and this paper is not exempt. When lacking enough CHB images, training a CNN from scratch would be very difficult and prone to overfitting; that's why we opted to use a technique called transfer learning (TL) in which we used pre-trained ResNet, MobileNet, and Inception networks, for classification. Even more, the Grad-CAM was utilized to localize the defects to some extent. The final results were very favorable based on those of similar research. The final proposed model can pave the way for moving from manual to unmanned CHB conservation, hence an increase in accuracy and a decrease in human-induced errors.

Artificial Intelligence (AI) weather prediction (AIWP) models are powerful tools for medium-range forecasts but often lack physical consistency, leading to outputs that violate conservation laws. This study introduces a set of novel physics-based schemes designed to enforce the conservation of global dry air mass, moisture budget, and total atmospheric energy in AIWP models. The schemes are highly modular, allowing for seamless integration into a wide range of AI model architectures. Forecast experiments are conducted to demonstrate the benefit of conservation schemes using FuXi, an example AIWP model, modified and adapted for 1.0-degree grid spacing. Verification results show that the conservation schemes can guide the model in producing forecasts that obey conservation laws. The forecast skills of upper-air and surface variables are also improved, with longer forecast lead times receiving larger benefits. Notably, large performance gains are found in the total precipitation forecasts, owing to the reduction of drizzle bias. The proposed conservation schemes establish a foundation for implementing other physics-based schemes in the future. They also provide a new way to integrate atmospheric domain knowledge into the design and refinement of AIWP models.

While multimodal large language models (LLMs) excel at dialogue, whether they can adequately parse the structure of conversation -- conversational roles and threading -- remains underexplored. In this work, we introduce a suite of tasks and release TV-MMPC, a new annotated dataset, for multimodal conversation structure understanding. Our evaluation reveals that while all multimodal LLMs outperform our heuristic baseline, even the best-performing model we consider experiences a substantial drop in performance when character identities of the conversation are anonymized. Beyond evaluation, we carry out a sociolinguistic analysis of 350,842 utterances in TVQA. We find that while female characters initiate conversations at rates in proportion to their speaking time, they are 1.2 times more likely than men to be cast as an addressee or side-participant, and the presence of side-participants shifts the conversational register from personal to social.

Recent Multi-Party Conversation (MPC) models typically rely on graph-based approaches to capture dialogue structures. However, these methods have limitations, such as information loss during the projection of utterances into structural embeddings and constraints in leveraging pre-trained language models directly. In this paper, we propose SS-MPC, a response generation model for MPC that eliminates the need for explicit graph structures. Unlike existing models that depend on graphs to analyze conversation structures, SS-MPC internally encodes the dialogue structure as a sequential input, enabling direct utilization of pre-trained language models. Experimental results show that SS-MPC achieves 15.60\% BLEU-1 and 12.44\% ROUGE-L score, outperforming the current state-of-the-art MPC response generation model by 3.91\%p in BLEU-1 and 0.62\%p in ROUGE-L. Additionally, human evaluation confirms that SS-MPC generates more fluent and accurate responses compared to existing MPC models.

A covariant formalism is used in order to examine the status of Maxwell equations and to unify the concept of balances, for all chemical engineering applications in relation with electrodynamics. The resulting formal structure serves as a discussion in studying the determinism of electromagnetic systems, and examining the theoretical foundations for a general classification of chemical engineering applications when non-conservative forces are concerned. A strategy for modeling such applications is then sketched and the balances for the main conserved and non-conserved extensive quantities are then summarized in their covariant and classical forms.

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.

Recent advances in image editing leverage latent diffusion models (LDMs) for versatile, text-prompt-driven edits across diverse tasks. Yet, maintaining pixel-level edge structures-crucial for tasks such as photorealistic style transfer or image tone adjustment-remains as a challenge for latent-diffusion-based editing. To overcome this limitation, we propose a novel Structure Preservation Loss (SPL) that leverages local linear models to quantify structural differences between input and edited images. Our training-free approach integrates SPL directly into the diffusion model's generative process to ensure structural fidelity. This core mechanism is complemented by a post-processing step to mitigate LDM decoding distortions, a masking strategy for precise edit localization, and a color preservation loss to preserve hues in unedited areas. Experiments confirm SPL enhances structural fidelity, delivering state-of-the-art performance in latent-diffusion-based image editing. Our code will be publicly released at https://github.com/gongms00/SPL.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.