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Reinforcement Learning · Multi-agent

Alexey Skrynnik, Anton Andreychuk, Anatolii Borzilov, Alexander Chernyavskiy, Konstantin Yakovlev, Aleksandr Panov

Multi-agent reinforcement learning (MARL) has recently excelled in solving challenging cooperative and competitive multi-agent problems in various environments, typically involving a small number of agents and full observability. Moreover, a range of crucial robotics-related tasks, such as multi-robot pathfinding, which have traditionally been approached with classical non-learnable methods (e.g., heuristic search), are now being suggested for solution using learning-based or hybrid methods. However, in this domain, it remains difficult, if not impossible, to conduct a fair comparison between classical, learning-based, and hybrid approaches due to the lack of a unified framework that supports both learning and evaluation. To address this, we introduce POGEMA, a comprehensive set of tools that includes a fast environment for learning, a problem instance generator, a collection of predefined problem instances, a visualization toolkit, and a benchmarking tool for automated evaluation. We also introduce and define an evaluation protocol that specifies a range of domain-related metrics, computed based on primary evaluation indicators (such as success rate and path length), enabling a fair multi-fold comparison. The results of this comparison, which involves a variety of state-of-the-art MARL, search-based, and hybrid methods, are presented.

Applications · Physics

Paul Garnier, Vincent Lannelongue, Jonathan Viquerat, Elie Hachem

We introduce a novel masked pre-training technique for graph neural networks (GNNs) applied to computational fluid dynamics (CFD) problems. By randomly masking up to 40\% of input mesh nodes during pre-training, we force the model to learn robust representations of complex fluid dynamics. We pair this masking strategy with an asymmetric encoder-decoder architecture and gated multi-layer perceptrons to further enhance performance. The proposed method achieves state-of-the-art results on seven CFD datasets, including a new challenging dataset of 3D intracranial aneurysm simulations with over 250,000 nodes per mesh. Moreover, it significantly improves model performance and training efficiency across such diverse range of fluid simulation tasks. We demonstrate improvements of up to 60\% in long-term prediction accuracy compared to previous best models, while maintaining similar computational costs. Notably, our approach enables effective pre-training on multiple datasets simultaneously, significantly reducing the time and data required to achieve high performance on new tasks.Through extensive ablation studies, we provide insights into the optimal masking ratio, architectural choices, and training strategies.

Deep Learning · Generative Models and Autoencoders

Scott Hawley

We provide an accessible introduction to flow-matching and rectified flow models, which are increasingly at the forefront of generative AI applications. Typical descriptions of them are often laden with extensive probability-math equations, which can form barriers to the dissemination and understanding of these models. Fortunately, before they were couched in probabilities, the mechanisms underlying these models were grounded in basic physics, which provides an alternative and highly accessible (yet functionally equivalent) representation of the processes involved.

Theory · Probabilistic Methods

YuQing Xie, Tess Smidt

Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry breaking occurs in many physical systems and we may obtain a less symmetric stable state from an initial highly symmetric one. Hence, it is imperative that we understand how to systematically break symmetry in ENNs. In this work, we propose a novel symmetry breaking framework that is fully equivariant and is the first which fully addresses spontaneous symmetry breaking. We emphasize that our approach is general and applicable to equivariance under any group. To achieve this, we introduce the idea of symmetry breaking sets (SBS). Rather than redesign existing networks, we design sets of symmetry breaking objects which we feed into our network based on the symmetry of our inputs and outputs. We show there is a natural way to define equivariance on these sets, which gives an additional constraint. Minimizing the size of these sets equates to data efficiency. We prove that minimizing these sets translates to a well studied group theory problem, and tabulate solutions to this problem for the point groups. Finally, we provide some examples of symmetry breaking to demonstrate how our approach works in practice. The code for these examples is available at \url{https://github.com/atomicarchitects/equivariant-SBS}.

Reinforcement Learning · Online

Allen Ren, Justin Lidard, Lars Ankile, Anthony Simeonov, Pulkit Agrawal, Anirudha Majumdar, Benjamin Burchfiel, Hongkai Dai, Max Simchowitz

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task.

Applications · Physics

Viggo Moro, Luiz Chamon

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable solutions, their accuracy is often tied to the use of computationally intensive fine meshes. Moreover, they do not naturally account for measurements or prior solutions, and any change in the problem parameters requires results to be fully recomputed. Neural network-based approaches, such as physics-informed neural networks and neural operators, offer a mesh-free alternative by directly fitting those models to the PDE solution. They can also integrate prior knowledge and tackle entire families of PDEs by simply aggregating additional training losses. Nevertheless, they are highly sensitive to hyperparameters such as collocation points and the weights associated with each loss. This paper addresses these challenges by developing a science-constrained learning (SCL) framework. It demonstrates that finding a (weak) solution of a PDE is equivalent to solving a constrained learning problem with worst-case losses. This explains the limitations of previous methods that minimize the expected value of aggregated losses. SCL also organically integrates structural constraints (e.g., invariances) and (partial) measurements or known solutions. The resulting constrained learning problems can be tackled using a practical algorithm that yields accurate solutions across a variety of PDEs, neural network architectures, and prior knowledge levels without extensive hyperparameter tuning and sometimes even at a lower computational cost.

Deep Learning · Large Language Models

Ming Zhong, Aston Zhang, Xuewei Wang, Rui Hou, Wenhan Xiong, Chenguang Zhu, Zhengxing Chen, Liang Tan, Chloe Bi, Mike Lewis 等

The development and evaluation of Large Language Models (LLMs) have largely focused on individual capabilities. However, this overlooks the intersection of multiple abilities across different types of expertise that are often required for real-world tasks, which we term **cross capabilities**. To systematically explore this concept, we first define seven core individual capabilities and then pair them to form seven common cross capabilities, each supported by a manually constructed taxonomy. Building on these definitions, we introduce *CrossEval*, a benchmark comprising 1,400 human-annotated prompts, with 100 prompts for each individual and cross capability. To ensure reliable evaluation, we involve expert annotators to assess 4,200 model responses, gathering 8,400 human ratings with detailed explanations to serve as reference examples. Our findings reveal that current LLMs consistently exhibit the ``Law of the Weakest Link,'' where cross-capability performance is significantly constrained by the weakest component. Across 58 cross-capability scores from 17 models, 38 scores are lower than all individual capabilities, while 20 fall between strong and weak, but closer to the weaker ability. These results highlight LLMs' underperformance in cross-capability tasks, emphasizing the need to identify and improve their weakest capabilities as a key research priority. The code, benchmarks, and evaluations are available on our [project website](https://www.llm-cross-capabilities.org).

Theory · Probabilistic Methods

David Dalton, Alan Lazarus, Hao Gao, Dirk Husmeier

We introduce a framework for designing boundary constrained Gaussian process (BCGP) priors for exact enforcement of linear boundary conditions, and apply it to the machine learning of (initial) boundary value problems involving linear partial differential equations (PDEs).In contrast to existing work, we illustrate how to design boundary constrained mean and kernel functions for all classes of boundary conditions typically used in PDE modelling, namely Dirichlet, Neumann, Robin and mixed conditions. Importantly, this is done in a manner which allows for both forward and inverse problems to be naturally accommodated. We prove that the BCGP kernel has a universal representational capacity under Dirichlet conditions, and establish a formal equivalence between BCGPs and boundary-constrained neural networks (BCNNs) of infinite width.Finally, extensive numerical experiments are performed involving several linear PDEs, the results of which demonstrate the effectiveness and robustness of BCGP inference in the presence of sparse, noisy data.

Applications · Computer Vision

Lu Sang, Zehranaz Canfes, Dongliang Cao, Florian Bernard, Daniel Cremers

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

Applications · Physics

Xiaoyuan Cheng, Yi He, Yiming Yang, Xiao Xue, Sibo Cheng, Daniel Giles, Xiaohang Tang, Yukun Hu

Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which significantly hinder accurate long-term forecasting. As a result, understanding long-term statistical behavior is far more valuable than focusing on short-term accuracy. While autoregressive deep sequence models have been applied to capture long-term behavior, they often lead to exponentially increasing errors in learned dynamics. To address this, we shift the focus from simple prediction errors to preserving an invariant measure in dissipative chaotic systems. These systems have attractors, where trajectories settle, and the invariant measure is the probability distribution on attractors that remains unchanged under dynamics. Existing methods generate long trajectories of dissipative chaotic systems by aligning invariant measures, but it is not always possible to obtain invariant measures for arbitrary datasets. We propose the Poincaré Flow Neural Network (PFNN), a novel operator learning framework designed to capture behaviors of chaotic systems without any explicit knowledge of the invariant measure. PFNN employs an auto-encoder to map the chaotic system to a finite-dimensional feature space, effectively linearizing the chaotic evolution. It then learns the linear evolution operators to match the physical dynamics by addressing two critical properties in dissipative chaotic systems: (1) contraction, the system’s convergence toward its attractors, and (2) measure invariance, trajectories on the attractors following a probability distribution invariant to the dynamics. Our experiments on a variety of chaotic systems, including Lorenz systems, Kuramoto-Sivashinsky equation and Navier–Stokes equation, demonstrate that PFNN has more accurate predictions and physical statistics compared to competitive baselines including the Fourier Neural Operator and the Markov Neural Operator.

Applications · Time Series

Phillip Si, Peng Chen

Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as the recently developed Ensemble Score Filters (EnSF) face significant challenges when dealing with high-dimensional and nonlinear Bayesian filtering problems with sparse observations, which are ubiquitous in real-world applications. In this paper, we propose a novel data assimilation method, Latent-EnSF, which leverages EnSF with efficient and consistent latent representations of the full states and sparse observations to address the joint challenges of high dimensionlity in states and high sparsity in observations for nonlinear Bayesian filtering. We introduce a coupled Variational Autoencoder (VAE) with two encoders to encode the full states and sparse observations in a consistent way guaranteed by a latent distribution matching and regularization as well as a consistent state reconstruction. With comparison to several methods, we demonstrate the higher accuracy, faster convergence, and higher efficiency of Latent-EnSF for two challenging applications with complex models in shallow water wave propagation and medium-range weather forecasting, for highly sparse observations in both space and time.

Applications · Physics

Brandon Zhao, Aviad Levis, Liam Connor, Pratul Srinivasan, Katherine Bouman

Weak gravitational lensing is the slight distortion of galaxy shapes caused primarily by the gravitational effects of dark matter in the universe. In our work, we seek to invert the weak lensing signal from 2D telescope images to reconstruct a 3D map of the universe’s dark matter field. While inversion typically yeilds a 2D projection of the dark matter field, accurate 3D maps of the dark matter distribution are essential for localizing structures of interest and testing theories of our universe. However, 3D inversion poses signficant challenges. First, unlike standard 3D reconstruction that relies on multiple viewpoints, in this case, images are only observed from a single viewpoint. This challenge can be partially addressed by observing how galaxy emitters throughout the volume are lensed. However, this leads to the second challenge: the shapes and exact locations of unlensed galaxies are unknown, and can only be estimated with a very large degree of uncertainty. This introduces an overwhelming amount of noise which nearly drowns out the lensing signal completely. Previous approaches tackle this by imposing strong assumptions about the structures in the volume. We instead propose a methodology using a gravitationally-constrained neural field to flexibly model the continuous matter distribution. We take an analysis-by-synthesis approach, optimizing the weights of the neural network through a fully differentiable physical forward model to reproduce the lensing signal present in image measurements. We showcase our method on simulations, including realistic simulated measurements of dark matter distributions that mimic data from upcoming telescope surveys. Our results show that our method can not only outperform previous methods, but importantly is also able to recover potentially surprising dark matter structures.

Applications · Robotics

Songming Liu, Lingxuan Wu, Bangguo Li, Hengkai Tan, Huayu Chen, Zhengyi Wang, Ke Xu, Hang Su, Jun Zhu

Bimanual manipulation is essential in robotics, yet developing foundation models is extremely challenging due to the inherent complexity of coordinating two robot arms (leading to multi-modal action distributions) and the scarcity of training data. In this paper, we present the Robotics Diffusion Transformer (RDT), a pioneering diffusion foundation model for bimanual manipulation. RDT builds on diffusion models to effectively represent multi-modality, with innovative designs of a scalable Transformer to deal with the heterogeneity of multi-modal inputs and to capture the nonlinearity and high frequency of robotic data. To address data scarcity, we further introduce a Physically Interpretable Unified Action Space, which can unify the action representations of various robots while preserving the physical meanings of original actions, facilitating learning transferrable physical knowledge. With these designs, we managed to pre-train RDT on the largest collection of multi-robot datasets to date and scaled it up to $1.2$B parameters, which is the largest diffusion-based foundation model for robotic manipulation. We finally fine-tuned RDT on a self-created multi-task bimanual dataset with over $6$K+ episodes to refine its manipulation capabilities. Experiments on real robots demonstrate that RDT significantly outperforms existing methods. It exhibits zero-shot generalization to unseen objects and scenes, understands and follows language instructions, learns new skills with just 1$\sim$5 demonstrations, and effectively handles complex, dexterous tasks. We refer to https://rdt-robotics.github.io/rdt-robotics/ for the code and videos.

Deep Learning · Generative Models and Autoencoders

Yuchen Lin, Chenguo Lin, Jianjin Xu, Yadong MU

Recently, significant advancements have been made in the reconstruction and generation of 3D assets, including static cases and those with physical interactions. To recover the physical properties of 3D assets, existing methods typically assume that all materials belong to a specific predefined category (e.g., elasticity). However, such assumptions ignore the complex composition of multiple heterogeneous objects in real scenarios and tend to render less physically plausible animation given a wider range of objects. We propose OmniPhysGS for synthesizing a physics-based 3D dynamic scene composed of more general objects. A key design of OmniPhysGS is treating each 3D asset as a collection of constitutive 3D Gaussians. For each Gaussian, its physical material is represented by an ensemble of 12 physical domain-expert sub-models (rubber, metal, honey, water, etc.), which greatly enhances the flexibility of the proposed model. In the implementation, we define a scene by user-specified prompts and supervise the estimation of material weighting factors via a pretrained video diffusion model. Comprehensive experiments demonstrate that OmniPhysGS achieves more general and realistic physical dynamics across a broader spectrum of materials, including elastic, viscoelastic, plastic, and fluid substances, as well as interactions between different materials. Our method surpasses existing methods by approximately 3% to 16% in metrics of visual quality and text alignment.

Applications · Physics

Philipp Scholl, Katharina Bieker, Hillary Hauger, Gitta Kutyniok

The problem of symbolic regression (SR) arises in many different applications, such as identifying physical laws or deriving mathematical equations describing the behavior of financial markets from given data. Various methods exist to address the problem of SR, often based on genetic programming. However, these methods are usually complicated and involve various hyperparameters. In this paper, we present our new approach ParFam that utilizes parametric families of suitable symbolic functions to translate the discrete symbolic regression problem into a continuous one, resulting in a more straightforward setup compared to current state-of-the-art methods. In combination with a global optimizer, this approach results in a highly effective method to tackle the problem of SR. We theoretically analyze the expressivity of ParFam and demonstrate its performance with extensive numerical experiments based on the common SR benchmark suit SRBench, showing that we achieve state-of-the-art results. Moreover, we present an extension incorporating a pre-trained transformer network (DL-ParFam) to guide ParFam, accelerating the optimization process by up to two magnitudes. Our code and results can be found at https://anonymous.4open.science/r/parfam-D402.

Applications · Physics

Sung Woong Cho, Hwijae Son

Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely on large amounts of labeled training data, which is impractical for most real-world applications. Moreover, these supervised models may fail to capture the underlying physical principles accurately. To address these limitations, we propose a novel architecture called Physics-Informed Deep Inverse Operator Networks (PI-DIONs), which can learn the solution operator of PDE-based inverse problems without any labeled training data. We extend the stability estimates established in the inverse problem literature to the operator learning framework, thereby providing a robust theoretical foundation for our method. These estimates guarantee that the proposed model, trained on a finite sample and grid, generalizes effectively across the entire domain and function space. Extensive experiments are conducted to demonstrate that PI-DIONs can effectively and accurately learn the solution operators of the inverse problems without the need for labeled data.

Applications · Physics

Aiqing Zhu, Yuting Pan, Qianxiao Li

Continuous dynamical systems are cornerstones of many scientific and engineering disciplines.While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as images, resulting in pixel-level observations that are discrete in nature.Consequently, a naive application of a convolutional autoencoder can result in latent coordinates that are discontinuous in time.To resolve this, we propose continuity-preserving convolutional autoencoders (CpAEs) to learn continuous latent states and their corresponding continuous latent dynamical models from discrete image frames. We present a mathematical formulation for learning dynamics from image frames, which illustrates issues with previous approaches and motivates our methodology based on promoting the continuity of convolution filters, thereby preserving the continuity of the latent states.This approach enables CpAEs to produce latent states that evolve continuously with the underlying dynamics, leading to more accurate latent dynamical models.Extensive experiments across various scenarios demonstrate the effectiveness of CpAEs.

Zaige Fei, Fan Xu, Junyuan Mao, Yuxuan Liang, Qingsong Wen, Kun Wang, Hao Wu, Yang Wang

In this paper, we use the Fire Dynamics Simulator (FDS) combined with the {\fontfamily{lmtt}\selectfont \textit{supercomputer}} support to create a \textbf{C}ombustion \textbf{K}inetics (CK) dataset for machine learning and scientific research. This dataset captures the development of fires in industrial parks with high-precision Computational Fluid Dynamics (CFD) simulations. It includes various physical fields such as temperature and pressure, and covers multiple environmental combinations for exploring \underline{multi-physics} field coupling phenomena. Additionally, we evaluate several advanced machine learning architectures across our {\fontfamily{lmtt}\selectfont {Open-CK}} benchmark using a substantial computational setup of 64 NVIDIA A100 GPUs: \ding{182} vision backbone; \ding{183} spatio-temporal predictive models; \ding{184} operator learning frameworks. These architectures uniquely excel at handling complex physical field data. We also introduce three benchmarks to demonstrate their potential in enhancing the exploration of downstream tasks: (a) capturing continuous changes in combustion kinetics; (b) a neural partial differential equation solver for learning temperature fields and turbulence; (c) reconstruction of sparse physical observations. The Open-CK dataset and benchmarks aim to advance research in combustion kinetics driven by machine learning, providing a reliable baseline for developing and comparing cutting-edge technologies and models. We hope to further promote the application of deep learning in earth sciences. Our project is available at \url{https://github.com/whscience/Open-CK}.

Deep Learning · Large Language Models

Minsung Kim, Jea Kwon, Dong-Kyum Kim, Meeyoung Cha

Large Language Models (LLMs) are enhancing our daily lives but also pose risks like spreading misinformation and violating privacy, highlighting the importance of understanding how they process and store information. This blogpost offers a fresh look into a neuroscience-inspired perspective of LLM's memory functions, based on the concept of engrams-the physical substrate of memory in living organism. We discuss a synergy between AI research and neuroscience, as both fields cover complexities of intelligent systems.

Applications · Physics

Bharat Srikishan, Daniel O'Malley, Mohamed Mehana, Nicholas Lubbers, Nikhil Muralidhar

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as `differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a model-agnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by **47%-78%**, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Code available at https://github.com/scailab/HyPER.