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Applications · Robotics

Ajay Sridhar, Jennifer Pan, Satvik Sharma, Chelsea Finn

Humans rely on memory to perform tasks; our goal is to endow robot policies with the same ability. Naively conditioning on long observation histories is computationally expensive and brittle under covariate shift, while indiscriminate subsampling of history leads to irrelevant or redundant information. We propose a hierarchical policy framework, where the high-level policy is trained to select and track previous task-relevant keyframes from its experience. The high-level policy uses selected keyframes and the most recent frames when generating text instructions for a low-level policy to execute. This design is compatible with existing vision-language-action (VLA) models and enables the system to efficiently reason over long-horizon dependencies. In our experiments, we fine-tune Qwen2.5-VL-7B-Instruct and $\pi_{0.5}$ as the high-level and low-level policies respectively, using demonstrations supplemented with minimal language annotations. Our approach, MemER, outperforms prior methods on three real-world long-horizon robotic manipulation tasks that require minutes of memory. Videos and code can be found at https://jen-pan.github.io/memer/.

Applications · Physics

Hao Tang, Hao Chen, Chao Li

Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that break rotational consistency. Existing spherical operators rely on rotational equivariance but often lack the flexibility for real-world complexity. We propose a generalized operator-design framework based on designable Green’s function and its harmonic expansion, establishing a solid operator-theoretic foundation for spherical learning. Based on this, we propose an absolute and relative position-dependent Green’s function that enables flexible balance of equivariance and invariance for real-world modeling. The resulting operator, Green's-function Spherical Neural Operator (GSNO) with a novel spectral learning method, can adapt to non-equivariant systems while retaining spherical geometry, spectral efficiency and grid invariance. To exploit GSNO, we develop SHNet, a hierarchical architecture that combines multi-scale spectral modeling with spherical up-down sampling, enhancing global feature representation. Evaluations on diffusion MRI, shallow water dynamics, and global weather forecasting, GSNO and SHNet consistently outperform state-of-the-art methods. The theoretical and experimental results position GSNO as a principled and generalized framework for spherical operator learning, bridging rigorous theory with real-world complexity. The code is available at: https://github.com/haot2025/GSNO.

Hao Wang, Yu Liu, Daniel Biggs, Haoru Wang, Jiandong Yu, Ping Huang

Simulating interactions between deformable bodies is vital in fields like material science, mechanical design, and robotics. While learning-based methods with Graph Neural Networks (GNNs) are effective at solving complex physical systems, they encounter scalability issues when modeling deformable body interactions. To model interactions between objects, pairwise global edges have to be created dynamically, which is computationally intensive and impractical for large-scale meshes. To overcome these challenges, drawing on insights from geometric representations, we propose an Adaptive Spatial Tokenization (AST) method for efficient representation of physical states. By dividing the simulation space into a grid of cells and mapping unstructured meshes onto this structured grid, our approach naturally groups adjacent mesh nodes. We then apply a cross-attention module to map the sparse cells into a compact, fixed-length embedding, serving as tokens for the entire physical state. Self-attention modules are employed to predict the next state over these tokens in latent space. This framework leverages the efficiency of tokenization and the expressive power of attention mechanisms to achieve accurate and scalable simulation results. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art approaches in modeling deformable body interactions. Notably, it remains effective on large-scale simulations with meshes exceeding 100,000 nodes, where existing methods are hindered by computational limitations. Additionally, we contribute a novel large-scale dataset encompassing a wide range of deformable body interactions to support future research in this area.

Computer Vision · Vision Models & Multimodal

Pengxiang Li, Yinan Zheng, Yue Wang, Huimin Wang, Hang Zhao, Jingjing Liu, Xianyuan Zhan, Kun Zhan, XianPeng Lang

End-to-End (E2E) solutions have emerged as a mainstream approach for autonomous driving systems, with Vision-Language-Action (VLA) models representing a new paradigm that leverages pre-trained multimodal knowledge from Vision-Language Models (VLMs) to interpret and interact with complex real-world environments. However, these methods remain constrained by the limitations of imitation learning, which struggles to inherently encode physical rules during training. Existing approaches often rely on complex rule-based post-refinement, employ reinforcement learning that remains largely limited to simulation, or utilize diffusion guidance that requires computationally expensive gradient calculations. To address these challenges, we introduce ReflectDrive, a novel learning-based framework that integrates a reflection mechanism for safe trajectory generation via discrete diffusion. We first discretize the two-dimensional driving space to construct an action codebook, enabling the use of pre-trained Diffusion Language Models for planning tasks through fine-tuning. Central to our approach is a safety-aware reflection mechanism that performs iterative self-correction without gradient computation. Our method begins with goal-conditioned trajectory generation to model multi-modal driving behaviors. Based on this, we apply local search methods to identify unsafe tokens and determine feasible solutions, which then serve as safe anchors for inpainting-based regeneration. Evaluated on the NAVSIM benchmark, ReflectDrive demonstrates significant advantages in safety-critical trajectory generation, offering a scalable and reliable solution for autonomous driving systems.

Applications · Language, Speech and Dialog

Zihan Liu, Zhikang Niu, Qiuyang Xiao, Zhisheng Zheng, Ruoqi Yuan, Yuhang Zang, Yuhang Cao, Xiaoyi Dong, Jianze Liang, Xie Chen 等

Despite rapid progress in Multi-modal Large Language Models and Large Audio-Language Models, existing audio benchmarks largely test semantics that can be recovered from text captions, masking deficits in fine-grained perceptual reasoning. We formalize audio 4D intelligence that is defined as reasoning over sound dynamics in time and 3D space, and introduce STAR-Bench to measure it. STAR-Bench combines a Foundational Acoustic Perception setting (six attributes under absolute and relative regimes) with a Holistic Spatio-Temporal Reasoning setting that includes segment reordering for continuous and discrete processes and spatial tasks spanning static localization, multi-source relations, and dynamic trajectories. Our data curation pipeline uses two methods to ensure high-quality samples. For foundational tasks, we use procedurally synthesized and physics-simulated audio. For holistic data, we follow a four-stage process that includes human annotation and final selection based on human performance. Unlike prior benchmarks where caption-only answering reduces accuracy slightly, STAR-Bench induces far larger drops (-31.5\% temporal, -35.2\% spatial), evidencing its focus on linguistically hard-to-describe cues. Evaluating 19 models reveals substantial gaps compared with humans and a capability hierarchy: closed-source models are bottlenecked by fine-grained perception, while open-source models lag across perception, knowledge, and reasoning. Our STAR-Bench provides critical insights and a clear path forward for developing future models with a more robust understanding of the physical world.

Computer Vision · 3D Rendering & Reconstruction

Kyu Beom Han, Jaeyoon Kim, Woo Jae Kim, Jinhwan Seo, Sung-eui Yoon

Inverse rendering with Gaussian Splatting has advanced rapidly, but accurately disentangling material properties from complex global illumination effects, particularly indirect illumination, remains a major challenge. Existing methods often query indirect radiance from Gaussian primitives pre-trained for novel-view synthesis. However, these pre-trained Gaussian primitives are supervised only towards limited training viewpoints, thus lack supervision for modeling indirect radiances from unobserved views. To address this issue, we introduce radiometric consistency, a novel physically-based constraint that provides supervision towards unobserved views by minimizing the residual between each Gaussian primitive’s learned radiance and its physically-based rendered counterpart. Minimizing the residual for unobserved views establishes a self-correcting feedback loop that provides supervision from both physically-based rendering and novel-view synthesis, enabling accurate modeling of inter-reflection. We then propose Radiometrically Consistent Gaussian Surfels (RadioGS), an inverse rendering framework built upon our principle by efficiently integrating radiometric consistency by utilizing Gaussian surfels and 2D Gaussian ray tracing. We further propose a finetuning-based relighting strategy that adapts Gaussian surfel radiances to new illuminations within minutes, achieving low rendering cost ($<$10ms). Extensive experiments on existing inverse rendering benchmarks show that RadioGS outperforms existing Gaussian-based methods in inverse rendering, while retaining the computational efficiency.

Computer Vision · 3D Rendering & Reconstruction

Sherwin Bahmani, Tianchang Shen, Jiawei Ren, Jiahui Huang, Yifeng Jiang, Haithem Turki, Andrea Tagliasacchi, David Lindell, Zan Gojcic, Sanja Fidler 等

The ability to generate virtual environments is crucial for applications ranging from gaming to physical AI domains such as robotics, autonomous driving, and industrial AI. Current learning-based 3D reconstruction methods rely on the availability of captured real-world multi-view data, which is not always readily available. Recent advancements in video diffusion models have shown remarkable imagination capabilities, yet their 2D nature prevents their use in simulations where a robot needs to navigate and interact with the environment. In this paper, we propose a self-distillation framework that aims to distill the implicit 3D knowledge in the video diffusion models into an explicit 3D Gaussian Splatting (3DGS) representation, eliminating the need for multi-view training data. Specifically, we augment the typical RGB decoder with a 3DGS decoder, which is supervised by the output of the RGB decoder. In this approach, the 3DGS decoder can be purely trained with synthetic data generated by video diffusion models. At inference time, our model can synthesize 3D scenes from either a text prompt or a single image for real-time rendering. Our framework further extends to dynamic 3D scene generation from a monocular input video. Experimental results show that our framework achieves state-of-the-art performance in static and dynamic 3D scene generation. Video results: https://research.nvidia.com/labs/toronto-ai/lyra

Computer Vision · 3D Rendering & Reconstruction

Daniel Wang, Patrick Rim, Tian Tian, Dong Lao, Alex Wong, Ganesh Sundaramoorthi

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.

Applications · Physics

Mansi Sakarvadia, Kareem Hegazy, Amin Totounferoush, Kyle Chard, Yaoqing Yang, Ian Foster, Michael W Mahoney

A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLO) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform “zero-shot super-resolution,” namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.

Applications · Chemistry and Drug Discovery

Xuan Zhang, Haiyang Yu, Chengdong Wang, Jacob Helwig, Shuiwang Ji, Xiaofeng Qian

We aim to learn wavefunctions simulated by time-dependent density functional theory (TDDFT), which can be efficiently represented as linear combination coefficients of atomic orbitals. In real-time TDDFT, the electronic wavefunctions of a molecule evolve over time in response to an external excitation, enabling first-principles predictions of physical properties such as optical absorption, electron dynamics, and high-order response. However, conventional real-time TDDFT relies on time-consuming propagation of all occupied states with fine time steps. In this work, we propose OrbEvo, which is based on an equivariant graph transformer architecture and learns to evolve the full electronic wavefunction coefficients across time steps. First, to account for external field, we design an equivariant conditioning to encode both strength and direction of external electric field and break the symmetry from SO(3) to SO(2). Furthermore, we design two OrbEvo models, OrbEvo-WF and OrbEvo-DM, using wavefunction pooling and density matrix as interaction method, respectively. Motivated by the central role of the density functional in TDDFT, OrbEvo-DM encodes the density matrix aggregated from all occupied electronic states into feature vectors via tensor contraction, providing a more intuitive approach to learn the time evolution operator. We adopt a training strategy specifically tailored to limit the error accumulation of time-dependent wavefunctions over autoregressive rollout. To evaluate our approach, we generate TDDFT datasets consisting of 5,000 different molecules in the QM9 dataset and 1,500 molecular configurations of the malonaldehyde molecule in the MD17 dataset. Results show that our OrbEvo model accurately captures quantum dynamics of excited states under external field, including time-dependent wavefunctions, time-dependent dipole moment, and optical absorption spectra characterized by dipole oscillator strength. It also shows strong generalization capability on the diverse molecules in the QM9 dataset. Our dataset is available at https://huggingface.co/divelab, and our code is available as part of the AIRS library https://github.com/divelab/AIRS/.

Jacob Helwig, Sai Adavi, Xuan Zhang, Yuchao Lin, Felix S Chim, Luke Vizzini, Haiyang Yu, Muhammad Hasnain, Saykat Biswas, John Holloway 等

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. We evaluate our methods by generating three supersonic flow datasets, available at https://huggingface.co/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Applications · Language, Speech and Dialog

Zhilin Wang, Jaehun Jung, Ximing Lu, Shizhe Diao, Ellie Evans, Jiaqi Zeng, Pavlo Molchanov, Yejin Choi, Jan Kautz, Yi Dong

Evaluating progress in large language models (LLMs) is often constrained by the challenge of verifying responses, limiting assessments to tasks like mathematics, programming, and short-form question-answering. However, many real-world applications require evaluating LLMs in processing professional documents, synthesizing information, and generating comprehensive reports in response to user queries. We introduce ProfBench: a set of over 7000 response-criterion pairs as evaluated by human-experts with professional knowledge across Physics PhD, Chemistry PhD, Finance MBA and Consulting MBA. We build robust and affordable LLM-Judges to evaluate ProfBench rubrics, by mitigating self-enhancement bias and reducing the cost of evaluation by 2-3 orders of magnitude, to make it fair and accessible to the broader community. Our findings reveal that ProfBench poses significant challenges even for state-of-the-art LLMs, with top-performing models like GPT-5-high achieving only 65.9\% overall performance. Furthermore, we identify notable performance disparities between proprietary and open-weight models and provide insights into the role that extended thinking plays in addressing complex, professional-domain tasks.

General Machine Learning · Representation Learning

Navami Kairanda, Shanthika Naik, Marc Habermann, Avinash Sharma, Christian Theobalt, Vladislav Golyanik

We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are, both, computationally intensive and slow to train. Although grid-based alternatives for implicit representations (e.g., Instant-NGP and K-Planes) train faster by exploiting signal structure, their reliance on linear interpolation restricts their ability to compute higher-order derivatives, rendering them unsuitable for solving DEs. In contrast, our approach overcomes these limitations by combining the efficiency of feature grids with radial basis function interpolation, which is infinitely often differentiable. To effectively capture high-frequency solutions and enable stable and faster computation of global gradients, we introduce a multi-resolution decomposition with co-located grids. Our proposed representation, $\boldsymbol{\partial^\infty}$-Grid, is trained implicitly using the differential equations as loss functions, enabling accurate modeling of physical fields. We validate $\boldsymbol{\partial^\infty}$-Grid on a variety of tasks, including Poisson equation for image reconstruction, the Helmholtz equation for wave fields, and the Kirchhoff-Love boundary value problem for cloth simulation. Our results demonstrate a 5–20× speed-up over coordinate-based MLP-based methods, solving differential equations in seconds or minutes while maintaining comparable accuracy and compactness.

Applications · Robotics

Suhwan Choi, Jaeyoon Jung, Haebin Seong, Minchan Kim, Minyeong Kim, Yongjun Cho, Yoonshik Kim, Yu Park, Youngjae Yu, Yunsung Lee

Large language models leverage internet-scale text data, yet embodied AI remains constrained by the prohibitive costs of physical trajectory collection. Desktop environments---particularly gaming---offer a compelling alternative: they provide rich sensorimotor interactions at scale while maintaining the structured observation-action coupling essential for embodied learning. We present D2E (Desktop to Embodied AI), a framework that demonstrates desktop interactions can serve as an effective pretraining substrate for robotics embodied AI tasks. Unlike prior work that remained domain-specific (e.g., VPT for Minecraft) or kept data proprietary (e.g., SIMA), D2E establishes a complete pipeline from scalable desktop data collection to verified transfer in embodied domains. Our framework comprises three components: (1) the OWA Toolkit that unifies diverse desktop interactions into a standardized format with 152× compression, (2) the Generalist-IDM that achieves strong zero-shot generalization across unseen games through timestamp-based event prediction, enabling internet-scale pseudo-labeling, and (3) VAPT that transfers desktop-pretrained representations to physical manipulation and navigation. Using 1.3K+ hours of data (259 hours of human demonstrations and 1K+ hours of pseudo-labeled gameplay), our 1B-parameter model achieves 96.6\% success on LIBERO manipulation and 83.3\% on CANVAS navigation, matching or surpassing models up to 7$\times$ larger, such as $\pi_0$ (3.3B) and OpenVLA (7B). These results demonstrate that sensorimotor primitives learned from digital interactions transfer effectively to real-world physical tasks, establishing desktop pretraining as a practical paradigm for embodied AI. All resources are publicly available at https://worv-ai.github.io/d2e.

Deep Learning · Graph Neural Networks

Winfried van den Dool, Maksim Zhdanov, Yuki Asano, Max Welling, Winfried van den Dool

Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions, they still apply uniform computational effort across all nodes regardless of the underlying physics complexity. This leads to inefficient resource allocation where computationally simple regions receive the same treatment as complex phenomena. We address this challenge by introducing Adaptive Mesh Quantization: spatially adaptive quantization across mesh node, edge and cluster features, dynamically adjusting the bit-width used by a quantized model. We propose an adaptive bit-width allocation strategy driven by a lightweight auxiliary model that identifies high-loss regions in the input mesh. This enables dynamic resource distribution in the main model, where regions of higher difficulty are allocated increased bit-width, optimizing computational resource utilization. We demonstrate our framework's effectiveness by integrating it with two state-of-the-art models, MP-PDE and GraphViT, to evaluate performance across multiple tasks: 2D Darcy flow, large-scale unsteady fluid dynamics in 2D, steady-state Navier–Stokes simulations in 3D, and a 2D hyper-elasticity problem. Our framework demonstrates consistent Pareto improvements over uniformly quantized baselines, yielding up to 50\% improvements in performance at the same cost.

Applications · Physics

Vladimir Fanaskov, Vladislav Trifonov, Alexander Rudikov, Ekaterina Muravleva, Ivan Oseledets

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of the problem. A practical way to apply such a scheme is to compute subspaces for a selected set of parameters in the computationally demanding offline stage and in the online stage approximate subspace for unknown parameters by interpolation. For realistic problems the space of parameters is high dimensional, which renders classical interpolation strategies infeasible or unreliable. We propose to relax the interpolation problem to regression, introduce several loss functions suitable for subspace data, and use a neural network as an approximation to high-dimensional target function. To further simplify a learning problem we introduce redundancy: in place of predicting subspace of a given dimension we predict larger subspace. We show theoretically that this strategy decreases the complexity of the mapping for elliptic eigenproblems with constant coefficients and makes the mapping smoother for general smooth function on the Grassmann manifold. Empirical results also show that accuracy significantly improves when larger-than-required subspaces are predicted. With the set of numerical illustrations we demonstrate that subspace regression can be useful for a range of tasks including parametric eigenproblems, deflation techniques, relaxation methods, optimal control and solution of parametric partial differential equations.

Computer Vision · Vision Models & Multimodal

Sihan Yang, Runsen Xu, Yiman Xie, Sizhe Yang, Mo Li, Jingli Lin, Chenming Zhu, Xiaochen Chen, Haodong Duan, Xiangyu Yue 等

Spatial intelligence is essential for multimodal large language models (MLLMs) operating in the complex physical world. Existing benchmarks, however, probe only single-image relations and thus fail to assess the multi-image spatial reasoning that real-world deployments demand. We introduce MMSI-Bench, a VQA benchmark dedicated to multi-image spatial intelligence. Six 3D-vision researchers spent more than 300 hours meticulously crafting 1,000 challenging, unambiguous multiple-choice questions from over 120,000 images, each paired with carefully designed distractors and a stepwise reasoning process. We conduct extensive experiments and evaluate 37 open-source and proprietary MLLMs, observing a wide gap: the strongest open-source model attains roughly 30\% accuracy and OpenAI's GPT-5 reasoning model reaches 40\%, while humans score 97\%. These results underscore the challenging nature of MMSI-Bench and the substantial headroom for future research. Leveraging the annotated reasoning processes, we also provide an automated error analysis pipeline that diagnoses four dominant failure modes, including (1) grounding errors, (2) overlap-matching and scene-reconstruction errors, (3) situation-transformation reasoning errors, and (4) spatial-logic errors, offering insights for advancing spatial intelligence.

Computer Vision · Everything Else

Rishit Dagli, Donglai Xiang, Vismay Modi, Charles Loop, Clement Fuji Tsang, Anka He Chen, Anita Hu, Gavriel State, David I.W., Maria Shugrina

Physical simulation relies on spatially-varying mechanical properties, typically laboriously hand-crafted. We present the first feed-forward model to predict fine-grained mechanical properties, Young’s modulus ($E$), Poisson’s ratio ($\nu$), and density ($\rho$), throughout *the volume* of 3D objects. Our model supports any 3D representation that can be rendered and voxelized, including Signed Distance Fields (SDFs), Gaussian Splats and Neural Radiance Fields (NeRFs). To achieve this, we aggregate per-voxel multi-view features for any input, which are passed to our trained Geometry Transformer to predict per-voxel material latent codes. These latents reside on the trained manifold of physically plausible materials, which we train on a real-world dataset, guaranteeing the validity of decoded per-voxel materials. To obtain object-level training data, we propose an annotation pipeline combining knowledge from segmented 3D datasets, material databases, and a vision-language model. Experiments show that VoMP estimates accurate volumetric properties and can convert 3D objects into simulation-ready assets, resulting in realistic deformable simulations and far outperforming prior art.

Deep Learning · Graph Neural Networks

Kai Yang, Yuqi Huang, Junheng Tao, Wanyu Wang, Qitian Wu

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant neural architecture for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory. Our codes, baseline models and datasets are available at https://github.com/Icarus1411/PAINET.

Applications · Robotics

XIAOHAN YE, Kui Wu, Taku Komura, zherong pan

With the maturation of differentiable physics, its role in various downstream applications—such as model-predictive control, robotic design optimization, and neural PDE solvers—has become increasingly important. However, the derivative information provided by differentiable simulators can exhibit abrupt changes or vanish altogether, impeding the convergence of gradient-based optimizers. In this work, we demonstrate that such erratic gradient behavior is closely tied to the design of contact models. We further introduce a set of properties that a contact model must satisfy to ensure well-behaved gradient information. Lastly, we present a practical contact model for differentiable rigid-body simulators that satisfies all of these properties while maintaining computational efficiency. Our experiments show that, even from simple initializations, our contact model can discover complex, contact-rich control signals, enabling the successful execution of a range of downstream locomotion and manipulation tasks.