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Applications · Physics

Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred Hamprecht

Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics. Current implementations rely on specialized layers, limiting architectural choices. We introduce Lorentz Local Canonicalization (LLoCa), a general framework that renders any backbone network exactly Lorentz-equivariant. Using equivariantly predicted local reference frames, we construct LLoCa-transformers and graph networks. We adapt a recent approach for geometric message passing to the non-compact Lorentz group, allowing propagation of space-time tensorial features. Data augmentation emerges from LLoCa as a special choice of reference frame. Our models achieve competitive and state-of-the-art accuracy on relevant particle physics tasks, while being $4\times$ faster and using $10\times$ fewer FLOPs.

Applications · Physics

Chenhui Xu, Dancheng Liu, Amir Nassereldine, Jinjun Xiong

Physics‑Informed Neural Networks (PINNs) often exhibit “failure modes” in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep loss barriers. We challenge this understanding by demonstrate that the real culprit is insufficient arithmetic precision: with standard FP32, the L‑BFGS optimizer prematurely satisfies its convergence test, freezing the network in a spurious failure phase. Simply upgrading to FP64 rescues optimization, enabling vanilla PINNs to solve PDEs without any failure modes. These results reframe PINN failure modes as precision‑induced stalls rather than inescapable local minima and expose a three‑stage training dynamic—un‑converged, failure, success—whose boundaries shift with numerical precision. Our findings emphasize that rigorous arithmetic precision is the key to dependable PDE solving with neural networks. Our code is available at Supplementary Material.

Applications · Physics

Takeshi Koshizuka, Issei Sato

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a discrete weak form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

Reinforcement Learning · Everything Else

Jiawen Yu, Hairuo Liu, Qiaojun Yu, Jieji Ren, Ce Hao, Haitong Ding, Guangyu Huang, Guofan Huang, Yan Song, Panpan Cai 等

Vision-Language-Action (VLA) models have advanced general-purpose robotic manipulation by leveraging pretrained visual and linguistic representations. However, they struggle with contact-rich tasks that require fine-grained control involving force, especially under visual occlusion or dynamic uncertainty. To address these limitations, we propose \textbf{ForceVLA}, a novel end-to-end manipulation framework that treats external force sensing as a first-class modality within VLA systems. ForceVLA introduces \textbf{FVLMoE}, a force-aware Mixture-of-Experts fusion module that dynamically integrates pretrained visual-language embeddings with real-time 6-axis force feedback during action decoding. This enables context-aware routing across modality-specific experts, enhancing the robot's ability to adapt to subtle contact dynamics. We also introduce \textbf{ForceVLA-Data}, a new dataset comprising synchronized vision, proprioception, and force-torque signals across five contact-rich manipulation tasks. ForceVLA improves average task success by 23.2\% over strong $\pi_0$-based baselines, achieving up to 80\% success in tasks such as plug insertion. Our approach highlights the importance of multimodal integration for dexterous manipulation and sets a new benchmark for physically intelligent robotic control. Code and data will be released at https://sites.google.com/view/forcevla2025/.

Applications · Physics

Siyi Chen, Yixuan Jia, Qing Qu, He Sun, Jeffrey Fessler

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman Filter, Particle Filter) presuppose full knowledge of the true dynamics, which is not always satisfied in practice, while purely data-driven solvers learn a deterministic mapping between observations and states and therefore miss the intrinsic stochasticity of real processes. Recently, score-based diffusion models have shown promise for DA by learning a global diffusion prior to represent stochastic dynamics. However, their one-shot generation lacks stepwise physical consistency and struggles with complex stochastic processes. To address these issues, we propose FlowDAS, a generative DA framework that employs stochastic interpolants to learn state transition dynamics through step-by-step stochastic updates. By incorporating observations into each transition, FlowDAS can produce stable, measurement-consistent forecasts. Experiments on Lorenz-63, Navier–Stokes super-resolution/sparse-observation scenarios, and large-scale weather forecasting—where dynamics are partly or wholly unknown—show that FlowDAS surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility. Our implementation is available at https://github.com/umjiayx/FlowDAS.

Applications · Physics

Nicolas Wolf, Leif Seute, Vsevolod Viliuga, Simon Wagner, Jan Stühmer, Frauke Gräter

Deep generative models have recently been proposed for sampling protein conformations from the Boltzmann distribution, as an alternative to often prohibitively expensive Molecular Dynamics simulations. However, current state-of-the-art approaches rely on fine-tuning pre-trained folding models and evolutionary sequence information, limiting their applicability and efficiency, and introducing potential biases. In this work, we propose a flow matching model for sampling protein conformations based solely on backbone geometry - BBFlow. We introduce a geometric encoding of the backbone equilibrium structure as input and propose to condition not only the flow but also the prior distribution on the respective equilibrium structure, eliminating the need for evolutionary information. The resulting model is orders of magnitudes faster than current state-of-the-art approaches at comparable accuracy, is transferable to multi-chain proteins, and can be trained from scratch in a few GPU days. In our experiments, we demonstrate that the proposed model achieves competitive performance with reduced inference time, across not only an established benchmark of naturally occurring proteins but also de novo proteins, for which evolutionary information is scarce or absent. BBFlow is available at https://github.com/graeter-group/bbflow.

Social Aspects · Trustworthy Machine Learning

Zhe Tao, Aditya V Thakur

In explainable AI, DNN gradients are used to interpret the prediction; in safety-critical control systems, gradients could encode safety constraints; in scientific-computing applications, gradients could encode physical invariants. While recent work on provable editing of DNNs has focused on input-output constraints, the problem of enforcing hard constraints on DNN gradients remains unaddressed. We present ProGrad, the first efficient approach for editing the parameters of a DNN to provably enforce hard constraints on the DNN gradients. Given a DNN $\mathcal{N}$ with parameters $\theta$, and a set $\mathcal{S}$ of pairs $(\mathrm{x}, \mathrm{Q})$ of input $\mathrm{x}$ and corresponding linear gradient constraints $\mathrm{Q}$, ProGrad finds new parameters $\theta'$ such that $\bigwedge_{(\mathrm{x}, \mathrm{Q}) \in \mathcal{S}} \frac{\partial}{\partial \mathrm{x}}\mathcal{N}(\mathrm{x}; \theta') \in \mathrm{Q}$ while minimizing the changes $\lVert\theta' - \theta\rVert$. The key contribution is a novel *conditional variable gradient* of DNNs, which relaxes the NP-hard provable gradient editing problem to a linear program (LP), enabling ProGrad to use an LP solver to efficiently and effectively enforce the gradient constraints. We experimentally evaluated ProGrad via enforcing (i) hard Grad-CAM constraints on ImageNet ResNet DNNs; (ii) hard Integrated Gradients constraints on Llama 3 and Qwen 3 LLMs; (iii) hard gradient constraints in training a DNN to approximate a target function as a proxy for safety constraints in control systems and physical invariants in scientific applications. The results highlight the unique capability of ProGrad in enforcing hard constraints on DNN gradients.

Applications · Physics

Ruoyan Li, Guancheng Wan, Zijie Huang, Zixiao Liu, Haixin Wang, Xiao Luo, Wei Wang, Yizhou Sun

Flow‐field reconstruction from sparse sensor measurements remains a central challenge in modern fluid dynamics, as the need for high‐fidelity data often conflicts with practical limits on sensor deployment. Existing deep learning–based methods have demonstrated promising results, but they typically depend on simplifying assumptions such as two‐dimensional domains, predefined governing equations, synthetic datasets derived from idealized flow physics, and unconstrained sensor placement. In this work, we address these limitations by studying flow reconstruction under realistic conditions and introducing a \emph{directional transport‐aware Graph Neural Network (GNN)} that explicitly encodes both flow directionality and information transport. We further show that conventional sensor placement strategies frequently yield suboptimal configurations. To overcome this, we propose a novel \emph{Two‐Step Constrained PPO} procedure for Proximal Policy Optimization (PPO), which jointly optimizes sensor layouts by incorporating flow variability and accounts for reconstruction model's performance disparity with respect to sensor placement. We conduct comprehensive experiments under realistic assumptions to benchmark the performance of our reconstruction model and sensor placement policy. Together, they achieve significant improvements over existing methods.

Optimization · Stochastic & Convex Optimization

Aleksey Minabutdinov, Patrick Cheridito

We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory, physics and economics. While traditional numerical methods suffer from the curse of dimensionality and become computationally intractable in high dimensions, more recent neural network-based approaches scale better, but have mostly been studied with the aim of solving optimal transport problems and require the solution of complicated optimization or max-min problems. Using an implicit Fenchel formulation of convex conjugation, our approach facilitates an efficient gradient-based framework for the minimization of approximation errors and, as a byproduct, also provides a posteriori error estimates for the approximation quality. Numerical experiments demonstrate our method's ability to deliver accurate results across different high-dimensional examples. Moreover, by employing symbolic regression with Kolmogorov–Arnold networks, it is able to obtain the exact convex conjugates of specific convex functions.

Tingting Dan, Zhihao Fan, Guorong Wu

Alzheimer’s disease (AD) is marked by cognitive decline along with the widespread of tau aggregates across the brain cortex. Due to the challenges of imaging pathology spreading flows *in vivo*, however, quantitative analysis on the cortical pathways of tau propagation and its interaction with the cascade of amyloid-beta (A$\beta$) plaques lags behind the experimental insights of underlying pathophysiological mechanisms. To address this challenge, we present a physics-informed neural network, empowered by mean-field theory, to uncover the biologically meaningful spreading pathways of tau aggregates between two longitudinal snapshots. Following the notion of `prion-like' mechanism in AD, we first formulate the dynamics of tau propagation as a mean-field game (MFG), where the spread of tau aggregate at each location (aka. agent) depends on the collective behavior of the surrounding agents as well as the potential field formed by amyloid burden. Given the governing equation of propagation dynamics, MFG reaches an equilibrium that allows us to model the evolution of tau aggregates as an optimal transport with the lowest cost in *Wasserstein* space. By leveraging the variational primal-dual structure in MFG, we propose a *Wasserstein*-1 Lagrangian generative adversarial network (GAN), in which a Lipschitz critic seeks the appropriate transport cost at the population level and a generator parameterizes the flow fields of optimal transport across individuals. Additionally, we incorporate a symbolic regression module to derive an explicit formulation capturing the A$\beta$-tau crosstalk. Experimental results on public neuroimaging datasets demonstrate that our explainable deep model not only yields precise and reliable predictions of future tau progression for unseen new subjects but also provides a new window to uncover new understanding of pathology propagation in AD through learning-based approaches.

Applications

Colin Kohler, Purvik Patel, Nathan Vaska, Justin Goodwin, Matthew Jones, Robert Platt, Rajmonda Caceres, Robin Walters

Many modeling tasks from disparate domains can be framed the same way, computing spherical signals from geometric inputs, for example, computing the radar response of different objects or navigating through an environment. This paper introduces G2Sphere, a general method for mapping object geometries to spherical signals. G2Sphere operates entirely in Fourier space, encoding geometric structure into latent Fourier features using equivariant neural networks and outputting the Fourier coefficients of the continuous target signal, which can be evaluated at any resolution. By utilizing a hybrid GNN-spherical CNN architecture, our method achieves much higher frequency output signal than comparable equivariant GNNs and avoids hand-engineered geometry features used previously by purely spherical methods. We perform experiments on various challenging domains including radar response modeling, aerodynamic drag prediction, and policy learning for manipulation and navigation. We find that G2Sphere outperforms competitive baselines in terms of accuracy and inference time, and we demonstrate that equivariance and Fourier features lead to improved sample efficiency and generalization.The source code is available at: https://github.com/ColinKohler/geometry2sphere.

Applications · Physics

Yimeng Chen, Piotr Piękos, Mateusz Ostaszewski, Firas Laakom, Jürgen Schmidhuber

Evaluating the scientific discovery capabilities of large language model based agents, particularly how they cope with varying environmental complexity and utilize prior knowledge, requires specialized benchmarks currently lacking in the landscape. To address this gap, we introduce PhysGym, a novel benchmark suite and simulation platform for rigorously assessing LLM-based scientific reasoning in interactive physics environments. PhysGym's primary contribution lies in its sophisticated control over the level of prior knowledge provided to the agent. This allows researchers to dissect agent performance along axes including the complexity of the problem and the prior knowledge levels. The benchmark comprises a suite of interactive simulations, where agents must actively probe environments, gather data sequentially under constraints and formulate hypotheses about underlying physical laws. PhysGym provides standardized evaluation protocols and metrics for assessing hypothesis accuracy and model fidelity. We demonstrate the benchmark's utility by presenting results from baseline LLMs, showcasing its ability to differentiate capabilities based on varying priors and task complexity.

Applications · Everything Else

Sebastian Joseph, Syed M. Husain, Stella Offner, Stéphanie Juneau, Paul Torrey, Adam Bolton, Juan Farias, Niall Gaffney, Greg Durrett, Junyi Jessy Li

Large Language Models (LLMs) are being explored for applications in scientific research, including their capabilities to synthesize literature, answer research questions, generate research ideas, and even conduct computational experiments.Ultimately, our goal is for these to help scientists derive novel scientific insights. In many areas of science, such insights often arise from processing and visualizing data to understand its patterns. However, evaluating whether an LLM-mediated scientific workflow produces outputs conveying the correct scientific insights is challenging to evaluate and has not been addressed in past work.We introduce AstroVisBench, the first benchmark for both scientific computing and visualization in the astronomy domain.AstroVisBench judges a language model’s ability to both (1) create astronomy-specific workflows to process and analyze data and (2) visualize the results of these workflows through complex plots.Our evaluation of visualizations uses a novel LLM-as-a-judge workflow, which is validated against annotation by five professional astronomers.Using AstroVisBench we present an evaluation of state-of-the-art language models, showing a significant gap in their ability to engage in astronomy research as useful assistants.This evaluation provides a strong end-to-end evaluation for AI scientists that offers a path forward for the development of visualization-based workflows, which are central to a broad range of domains from physics to biology.

Meng-Hao Guo, Xuanyu Chu, Qianrui Yang, Zhe-Han Mo, Yiqing Shen, Pei-lin Li, Xinjie Lin, Jinnian Zhang, Xin-Sheng Chen, Yi Zhang 等

The rapid advancement of native multi-modal models and omni-models, exemplified by GPT-4o, Gemini and o3 with their capability to process and generate content across modalities such as text and images, marks a significant milestone in the evolution of intelligence. Systematic evaluation of their multi-modal output capabilities in visual thinking process (a.k.a., multi-modal chain of thought, M-CoT) becomes critically important. However, existing benchmarks for evaluating multi-modal models primarily focus on assessing multi-modal inputs and text-only reasoning process while neglecting the importance of reasoning through multi-modal outputs. In this paper, we present a benchmark, dubbed as RBench-V, designed to assess models’ vision-indispensable reasoning. To conduct RBench-V, we carefully hand-pick 803 questions covering math, physics, counting and games. Unlike problems in previous benchmarks, which typically specify certain input modalities, RBench-V presents problems centered on multi-modal outputs, which require image manipulation, such as generating novel images and constructing auxiliary lines to support reasoning process. We evaluate numerous open- and closed-source models on RBench-V, including o3, Gemini 2.5 pro, Qwen2.5-VL, etc. Even the best-performing model, o3, achieves only 25.8% accuracy on RBench-V, far below the human score of 82.3%, which shows current models struggle to leverage multi-modal reasoning. Data and code are available at https://evalmodels.github.io/rbenchv.

Computer Vision · Vision Models & Multimodal

Han Yi, Yulu Pan, Feihong He, Xinyu Liu, Benjamin Zhang, Oluwatumininu Oguntola, Gedas Bertasius

We present ExAct, a new video-language benchmark for expert-level understanding of skilled physical human activities. Our new benchmark contains 3,521 expert-curated video question-answer pairs spanning 11 physical activities in 6 domains: Sports, Bike Repair, Cooking, Health, Music, and Dance. ExAct requires the correct answer to be selected from five carefully designed candidate options, thus necessitating a nuanced, fine-grained, expert-level understanding of physical human skills. Evaluating the recent state-of-the-art VLMs on ExAct reveals a substantial performance gap relative to human expert performance. Specifically, the best-performing Gemini 2.5 Pro model achieves only 55.35% accuracy, well below the 82.02% attained by trained human experts. We believe that ExAct will be beneficial for developing and evaluating VLMs capable of precise understanding of human skills in various physical and procedural domains. Dataset and code are available at https://texaser.github.io/exact_project_page/.

Deep Learning · Generative Models and Autoencoders

Florian Felten, Gabriel Apaza, Gerhard Bräunlich, Cashen Diniz, Xuliang Dong, Arthur Drake, Milad Habibi, Nathaniel Hoffman, Matthew Keeler, Soheyl Massoudi 等

Engineering design optimization seeks to automatically determine the shapes, topologies, or parameters of components that maximize performance under given conditions. This process often depends on physics-based simulations, which are difficult to install, computationally expensive, and require domain-specific expertise. To mitigate these challenges, we introduce EngiBench, the first open‐source library and datasets spanning diverse domains for data‐driven engineering design. EngiBench provides a unified API and a curated set of benchmarks---covering aeronautics, heat conduction, photonics, and more---that enable fair, reproducible comparisons of optimization and machine learning algorithms, such as generative or surrogate models. We also release EngiOpt, a companion library offering a collection of such algorithms compatible with the EngiBench interface. Both libraries are modular, letting users plug in novel algorithms or problems, automate end-to-end experiment workflows, and leverage built-in utilities for visualization, dataset generation, feasibility checks, and performance analysis. We demonstrate their versatility through experiments comparing state-of-the-art techniques across multiple engineering design problems, an undertaking that was previously prohibitively time-consuming to perform. Finally, we show that these problems pose significant challenges for standard machine learning methods due to highly sensitive and constrained design manifolds.

Applications · Physics

Rishal Aggarwal, Jacky Chen, Nicholas Boffi, David Koes

Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to transform a simple prior into a distribution that can be reweighted to match the target using sample likelihoods. Despite the elegance of this approach, obtaining these likelihoods requires computing costly Jacobians during integration, which is impractical for large molecular systems. To overcome this difficulty, we train an energy-based model (EBM) to approximate likelihoods using both noise contrastive estimation (NCE) and score matching, which we show outperforms the use of either objective in isolation. On 2D synthetic systems where failure can be easily visualized, NCE improves mode weighting relative to score matching alone. On alanine dipeptide, our method yields free energy profiles and energy distributions that closely match those obtained using exact likelihoods while achieving $100\times$ faster inference. By training on multiple dipeptide systems, we show that our approach also exhibits effective transfer learning, generalizing to new systems at inference time and achieving at least a $6\times$ speedup over standard MD with only a bit of fine-tuning. While many recent efforts in generative modeling have prioritized models with fast sampling, our work demonstrates the design of models with accelerated likelihoods, enabling the application of reweighting schemes that ensure unbiased Boltzmann statistics at scale. Our code is available at https://github.com/RishalAggarwal/BoltzNCE.

Applications · Physics

Mouadh Yagoubi, David Danan, Milad LEYLI ABADI, Jocelyn Mazari, Jean-Patrick Brunet, Abbas Kabalan, Fabien Casenave, Yuxin Ma, Giovanni Catalani, Jean Fesquet 等

The integration of machine learning (ML) into the physical sciences is reshaping computational paradigms, offering the potential to accelerate demanding simulations such as computational fluid dynamics (CFD). Yet, persistent challenges in accuracy, generalization, and physical consistency hinder the practical deployment of ML models in scientific domains. To address these limitations and systematically benchmark progress, we organized the ML4CFD competition, centered on surrogate modeling for aerodynamic simulations over two-dimensional airfoils. The competition attracted over 240 teams, who were provided with a curated dataset generated via OpenFOAM and evaluated through a multi-criteria framework encompassing predictive accuracy, physical fidelity, computational efficiency, and out-of-distribution generalization. This retrospective analysis reviews the competition outcomes, highlighting several approaches that outperformed baselines under our global evaluation score. Notably, the top entry exceeded the performance of the original OpenFOAM solver on aggregate metrics, illustrating the promise of ML based surrogates to outperform traditional solvers under tailored criteria. However, this does not imply that the winning solution could replace the OpenFOAM solver or that it was overall superior, even for this specific task. Drawing from these results, we analyze the key design principles of top submissions, assess the robustness of our evaluation framework, and offer guidance for future scientific ML challenges.

Applications · Physics

Yuan Chiang, Tobias Kreiman, Christine Zhang, Matthew Kuner, Elizabeth Weaver, Ishan Amin, Hyunsoo Park, Yunsung Lim, Jihan Kim, Daryl Chrzan 等

Machine learning interatomic potentials (MLIPs) have revolutionized molecular and materials modeling, but existing benchmarks suffer from data leakage, limited transferability, and an over-reliance on error-based metrics tied to specific density functional theory (DFT) references. We introduce MLIP Arena, a benchmark platform that evaluates force field performance based on physics awareness, chemical reactivity, stability under extreme conditions, and predictive capabilities for thermodynamic properties and physical phenomena. By moving beyond static DFT references and revealing the important failure modes of current foundation MLIPs in real-world settings, MLIP Arena provides a reproducible framework to guide the next-generation MLIP development toward improved predictive accuracy and runtime efficiency while maintaining physical consistency. The Python package and online leaderboard are available at https://github.com/atomind-ai/mlip-arena.

Applications · Physics

Rui Yang, Ziruo Wang, Yuntian Gu, Yitao Liang, Tongyang Li

Quantum computing is an emerging field recognized for the significant speedup it offers over classical computing through quantum algorithms. However, designing and implementing quantum algorithms pose challenges due to the complex nature of quantum mechanics and the necessity for precise control over quantum states. Despite the significant advancements in AI, there has been a lack of datasets specifically tailored for this purpose. In this work, we introduce QCircuitBench, the first benchmark dataset designed to evaluate AI's capability in designing and implementing quantum algorithms in the form of quantum circuit codes. Unlike using AI for writing traditional codes, this task is fundamentally more complicated due to highly flexible design space. Our key contributions include: 1. A general framework which formulates the key features of quantum algorithm design task for Large Language Models.2. Implementation for quantum algorithms from basic primitives to advanced applications, spanning 3 task suites, 25 algorithms, and 120,290 data points.3. Automatic validation and verification functions, allowing for iterative and interactive evaluation without human inspection.4. Promising potential as a training dataset through primitive fine-tuning results.We observed several interesting experimental phenomena: fine-tuning does not always outperform few-shot learning, and LLMs tend to exhibit consistent error patterns. QCircuitBench provides a comprehensive benchmark for AI-driven quantum algorithm design, while also revealing some limitations of LLMs in this domain.