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Applications · Physics

Nan Jiang, Ziyi Wang, Yexiang Xue

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression renders the task computationally challenging. A promising yet underexplored direction for reducing the search space and accelerating training lies in *symbolic equivalence*: many expressions, although syntactically different, define the same function -- for example, $\log(x_1^2x_2^3)$, $\log(x_1^2)+\log(x_2^3)$, and $2\log(x_1)+3\log(x_2)$. Existing algorithms treat such variants as distinct outputs, leading to redundant exploration and slow learning. We introduce EGG-SR, a unified framework that integrates symbolic equivalence into a class of modern symbolic regression methods, including Monte Carlo Tree Search (MCTS), Deep Reinforcement Learning (DRL), and Large Language Models (LLMs). \method-SR compactly represents equivalent expressions through the proposed EGG module (via equality graphs), accelerating learning by: (1) pruning redundant subtree exploration in EGG-MCTS, (2) aggregating rewards across equivalent generated sequences in EGG-DRL, and (3) enriching feedback prompts in EGG-LLM. Theoretically, we show the benefit of embedding EGG into learning: it tightens the regret bound of MCTS and reduces the variance of the DRL gradient estimator. Empirically, EGG-SR consistently enhances a class of symbolic regression models across several benchmarks, discovering more accurate expressions within the same time limit. Project page is at: https://nan-jiang-group.github.io/egg-sr.

General Machine Learning · Probabilistic Methods

Zifan Wang, Alice Harting, Matthieu Barreau, Michael Zavlanos, Karl H. Johansson

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

Theory · Interpretability and Visualization

Tianxiang Dai, Jonathan Fan

Multi-Resolution Hash Encoding (MHE), the foundational technique behind Instant Neural Graphics Primitives, provides a powerful parameterization for neural fields. However, its spatial behavior lacks rigorous understanding from a physical systems perspective, leading to reliance on heuristics for hyperparameter selection. This work introduces a novel analytical approach that characterizes MHE by examining its Point Spread Function (PSF), which is analogous to the Green's function of the system. This methodology enables a quantification of the encoding's spatial resolution and fidelity. We derive a closed-form approximation for the collision-free PSF, uncovering inherent grid-induced anisotropy and a logarithmic spatial profile. We establish that the idealized spatial bandwidth, specifically the Full Width at Half Maximum (FWHM), is determined by the average resolution, $N_{\text{avg}}$. This leads to a counterintuitive finding: the effective resolution of the model is governed by the broadened empirical FWHM (and therefore $N_{\text{avg}}$), rather than the finest resolution $N_{\max}$, a broadening effect we demonstrate arises from optimization dynamics. Furthermore, we analyze the impact of finite hash capacity, demonstrating how collisions introduce speckle noise and degrade the Signal-to-Noise Ratio (SNR). Leveraging these theoretical insights, we propose Rotated MHE (R-MHE), an architecture that applies distinct rotations to the input coordinates at each resolution level. R-MHE mitigates anisotropy while maintaining the efficiency and parameter count of the original MHE. This study establishes a methodology based on physical principles that moves beyond heuristics to characterize and optimize MHE.

Computer Vision · Image and Video Generation

Yu Yuan, Xijun Wang, Tharindu Wickremasinghe, Zeeshan Nadir, Bole Ma, Stanley Chan

A primary bottleneck in large-scale text-to-video generation today is physical consistency and controllability. Despite recent advances, state-of-the-art models often produce unrealistic motions, such as objects falling upward, or abrupt changes in velocity and direction. Moreover, these models lack precise parameter control, struggling to generate physically consistent dynamics under different initial conditions. We argue that this fundamental limitation stems from current models learning motion distributions solely from appearance, while lacking an understanding of the underlying dynamics. In this work, we propose NewtonGen, a framework that integrates data-driven synthesis with learnable physical principles. At its core lies trainable Neural Newtonian Dynamics (NND), which can model and predict a variety of Newtonian motions, thereby injecting latent dynamical constraints into the video generation process. By jointly leveraging data priors and dynamical guidance, NewtonGen enables physically consistent video synthesis with precise parameter control. All data and code are available at https://github.com/pandayuanyu/NewtonGen.

Applications · Physics

Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma, Kallol Bera, Shahid Rauf, Kookjin Lee

Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited. We extend Fourier neural operators (FNOs) with minimal architectural modifications along two directions. For parameterized dynamics, we propose a hypernetwork-based modulation that conditions the operator on physical parameters. For coupled systems, we conduct a systematic exploration of architectural choices, examining how operator components can be adapted to balance shared structure with cross-variable interactions while retaining the efficiency of standard FNOs. Evaluations on benchmark PDEs, including the one-dimensional capacitively coupled plasma equations and the Gray–Scott system, show that our methods achieve up to 55~72% lower errors than strong baselines, demonstrating the effectiveness of principled modulation and systematic design exploration.

Applications · Everything Else

Yu Wang, Yi Wang, Rui Dai, Yujie Wang, Kaikui Liu, Xiangxiang Chu, Yansheng Li

As hubs of human activity, urban surfaces consist of a wealth of semantic entities. Segmenting these various entities from satellite imagery is crucial for a range of downstream applications. Current advanced segmentation models can reliably segment entities defined by physical attributes (e.g., buildings, water bodies) but still struggle with socially defined categories (e.g., schools, parks). In this work, we achieve socio-semantic segmentation by vision-language model reasoning. To facilitate this, we introduce the Urban Socio-Semantic Segmentation dataset named SocioSeg, a new resource comprising satellite imagery, digital maps, and pixel-level labels of social semantic entities organized in a hierarchical structure. Additionally, we propose a novel vision-language reasoning framework called SocioReasoner that simulates the human process of identifying and annotating social semantic entities via cross-modal recognition and multi-stage reasoning. We employ reinforcement learning to optimize this non-differentiable process and elicit the reasoning capabilities of the vision-language model. Experiments demonstrate our approach's gains over state-of-the-art models and strong zero-shot generalization. The dataset and code are open-sourced under the Apache License 2.0 at https://github.com/AMAP-ML/SocioReasoner.

Gabrijel Boduljak, Laurynas Karazija, Iro Laina, Christian Rupprecht, Andrea Vedaldi

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

Deep Learning · Algorithms

Zijin Liu, Xu Geng, Wenshuai Xu, Xiang Zhao, Yan Xia, You Song

Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual trajectories, are limited in their ability to capture macroscopic physical laws. This microscopic approach often leads to error accumulation and compromises simulation stability. Furthermore, deep learning-driven methods tend to suffer from low inference efficiency and high computational overhead, making them impractical for large-scale, efficient simulations. To address these challenges, we propose the Spatio-Temporal Decoupled Differential Equation Network (STDDN), a novel framework that guides microscopic trajectory prediction with macroscopic physics. We innovatively introduce the continuity equation from fluid dynamics as a strong physical constraint. A Neural Ordinary Differential Equation (Neural ODE) is employed to model the macroscopic density evolution driven by individual movements, thereby physically regularizing the microscopic trajectory prediction model. We design a density-velocity coupled dynamic graph learning module to formulate the derivative of the density field within the Neural ODE, effectively mitigating error accumulation. We also propose a differentiable density mapping module to eliminate discontinuous gradients caused by discretization and introduce a cross-grid detection module to accurately model the impact of individual cross-grid movements on local density changes. The proposed STDDN method has demonstrated significantly superior simulation performance compared to state-of-the-art methods on long-term tasks across four real-world datasets, as well as a major reduction in inference latency.

Applications · Robotics

Shivansh Patel, Shraddhaa Mohan, Hanlin Mai, Unnat Jain, Svetlana Lazebnik, Yunzhu Li

This work introduces Robots Imitating Generated Videos (RIGVid), a system that enables robots to perform complex manipulation tasks—such as pouring, wiping, and mixing—purely by imitating AI-generated videos, without requiring any physical demonstrations or robot-specific training. Given a language command and an initial scene image, a video diffusion model generates potential demonstration videos, and a vision-language model (VLM) automatically filters out results that do not follow the command. A 6D pose tracker then extracts object trajectories from the video, and the trajectories are retargeted to the robot in an embodiment-agnostic fashion. Through extensive realworld evaluations, we show that filtered generated videos are as effective as real demonstrations, and that performance improves with generation quality. We also show that relying on generated videos outperforms more compact alternatives such as keypoint prediction using VLMs, and that strong 6D pose tracking outperforms other ways to extract trajectories, such as dense feature point tracking. These findings suggest that videos produced by a state-of-the-art off-the-shelf model can offer an effective source of supervision for robotic manipulation.

Applications · Physics

Jiawen Zou, Weimin Tan, Zhongyao Wang, Hao Qi, Bo Yan

The message passing–readout framework has become the de facto standard of graph neural networks (GNNs) for material property prediction. However, most existing readout functions are built on an atom-decomposable inductive bias, i.e. the material-level property or feature can be reasonably assigned to contributions of individual atoms. This is a strong bias and may not hold for all properties, limiting the application scenarios (e.g. gas adsorption or separation of Metal Organic Frameworks, MOFs). In this work, we propose a region-based decomposition perspective, reformulating material properties as integrals over space and pooling contributions from spatial regions rather than atoms. Specifically, we propose a novel readout function named SpatialRead. SpatialRead introduces additional spatial nodes to represent a voxelized space, transforming the atomic isomorphic graph into a heterogeneous atom–space graph with unidirectional message flow from atoms to spatial nodes. To combine the two types of inductive bias, multimodal methods can be used to fuse the features of atoms the spatial nodes. Such a region-based readout function is especially suited for spatial properties such as gas adsorption capacity, separation ratio. Extensive experiments demonstrate that a simple PaiNN–Transformer-based SpatialRead trained from scratch outperforms state-of-the-art pre-trained foundation models on these special tasks. Our results highlight the importance of designing physically grounded readout functions tailored to the target property. The code and dataset can be found in github https://github.com/nankusa/SpatialRead.

Applications · Robotics

Sandeep Kumar Routray, Hengkai Pan, Unnat Jain, Shikhar Bahl, Deepak Pathak

Can we turn a video prediction model into a robot policy? Videos, including those of humans or teleoperated robots, capture rich physical interactions. However, most of them lack labeled actions, which limits their use in robot learning. We present *Video Prediction for Robot Actions* (**ViPRA**), a simple pretraining-finetuning framework that learns continuous robot control from these actionless videos. Instead of directly predicting actions, we train a video-language model to predict *both future visual observations and motion-centric latent actions*, which serve as intermediate representations of scene dynamics. We train these latent actions using perceptual losses and optical flow consistency to ensure they reflect physically grounded behavior. For downstream control, we introduce a chunked *flow-matching decoder* that maps latent actions to robot-specific continuous action sequences, using only 100 to 200 teleoperated demonstrations. This approach avoids expensive action annotation, supports generalization across embodiments, and enables smooth, high-frequency continuous control upto 22 Hz via chunked action decoding. Unlike prior latent action works that treat pretraining as autoregressive policy learning, ViPRA explicitly models both what changes and how. Our method outperforms strong baselines, with a 16% gain on the SIMPLER benchmark and a 13% improvement across real world manipulation tasks. We have released models and code [here](https://vipra-project.github.io/).

General Machine Learning · Representation Learning

Shiqian Li, Ruihong Shen, Yaoyu Tao, Chi Zhang, Yixin Zhu

Physical reasoning is a remarkable human ability that enables rapid learning and generalization from limited experience. Current AI models, despite extensive training, still struggle to achieve similar generalization, especially in Out-of-distribution (OOD) settings. This limitation stems from their inability to abstract core physical principles from observations. A key challenge is developing representations that can efficiently learn and generalize physical dynamics from minimal data. Here we present Neural Force Field (NFF), a framework extending Neural Ordinary Differential Equation (NODE) to learn complex object interactions through force field representations, which can be efficiently integrated through an Ordinary Differential Equation ( ODE) solver to predict object trajectories. Unlike existing approaches that rely on discrete latent spaces, NFF captures fundamental physical concepts such as gravity, support, and collision in continuous explicit force fields. Experiments on three challenging physical reasoning tasks demonstrate that NFF, trained with only a few examples, achieves strong generalization to unseen scenarios. This physics-grounded representation enables efficient forward-backward planning and rapid adaptation through interactive refinement. Our work suggests that incorporating physics-inspired representations into learning systems can help bridge the gap between artificial and human physical reasoning capabilities.

Applications · Physics

Zeyuan Song, Zheyu Jiang

Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications. In this paper, we propose Adaptive Mamba Neural Operators (AMO), which integrates reproducing kernels for state-space models (SSMs) rather than the kernel integral formulation of SSMs. This is achieved by constructing Takenaka-Malmquist systems for the PDEs. AMO offers new representations that align well with the adaptive Fourier decomposition (AFD) theory and can approximate the solution manifold of PDEs on a wide range of geometries and meshes. In several challenging benchmark PDE problems in the fields of fluid physics, solid physics, and finance on point clouds, structured meshes, regular grids, and irregular domains, AMO consistently outperforms state-of-the-art solvers in terms of relative $L^2$ error. Overall, this work presents a new paradigm for designing explainable neural operator frameworks. The code is available at https://github.com/checlams/AMO.

Applications · Chemistry and Drug Discovery

Ngoc-Quang Nguyen, Jaeyoon Jung, Seijung Kim, Sunkyu Kim, Jaewoo Kang

Peptides, short chains of amino acids capable of high-specificity protein binding, represent a powerful class of therapeutics. While deep generative models have shown promise for peptide design, existing approaches are often structure-centric and therefore generate sequences and structures in a decoupled manner, failing to ensure that designs are simultaneously physically stable, evolutionarily plausible, and internally coherent. To overcome this limitation, we introduce \textbf{PepTri}, a novel diffusion framework that addresses this by jointly generating peptide sequences and 3D structures within a unified, SE(3)-equivariant latent space. Our proposed model integrates three complementary guidance signals during the generative process: (i) physics-informed guidance via differentiable molecular mechanics to ensure structural stability and realism; (ii) evolutionary guidance to bias sequences toward conserved, functional motifs; and (iii) mutual information guidance to explicitly maximize sequence-structure coherence. This tri-guided approach ensures the generative process is steered by biophysical laws, biological priors, and information-theoretic alignment in tandem. Extensive evaluations on challenging peptide-protein design benchmarks, cross-domain (PepBench, LNR) and in-domain (PepBDB), demonstrate that PepTri substantially outperforms strong baselines, achieving state-of-the-art results in binding affinity, structural accuracy, and design diversity. Our results establish that integrating these complementary signals directly into the denoising process is crucial for generating viable, high-quality peptide medicines. PepTri is available at: https://github.com/aigensciences/PepTri

Computer Vision · Image and Video Generation

Shan Wang, Peixia Li, Chenchen Xu, Ziang Cheng, Jiayu Yang, Hongdong Li, Pulak Purkait

We propose Light–Geometry Interaction (LGI) maps, a novel representation that encodes light-aware occlusion from monocular depth. Unlike ray tracing, which requires full 3D reconstruction, LGI captures essential light–shadow interactions reliably and accurately, computed from off-the-shelf 2.5D depth map predictions. LGI explicitly ties illumination direction to geometry, providing a physics-inspired prior that constrains generative models. Without such prior, these models often produce floating shadows, inconsistent illumination, and implausible shadow geometry. Building on this representation, we propose a unified pipeline for joint shadow generation and relighting-unlike prior methods that treat them as disjoint tasks-capturing the intrinsic coupling of illumination and shadowing essential for modeling indirect effects. By embedding LGI into a bridge-matching generative backbone, we reduce ambiguity and enforce physically consistent light–shadow reasoning. To enable effective training, we curated the first large-scale benchmark dataset for joint shadow and relighting, covering reflections, transparency, and complex interreflections. Experiments show significant gains in realism and consistency across synthetic and real images. LGI thus bridges geometry-inspired rendering with generative modeling, enabling efficient, physically consistent shadow generation and relighting.

Computer Vision · Vision Models & Multimodal

Hanyu Zhou, Gim H Lee

Despite achieving significant progress in 2D image understanding, large multimodal models (LMMs) struggle in the physical world due to the lack of spatial representation. Typically, existing 3D LMMs mainly embed 3D positions as fixed spatial prompts within visual features to represent the scene. However, these methods are limited to understanding the static background and fail to capture temporally varying dynamic objects. In this work, we propose LLaVA-4D, a general LMM framework with a novel spatiotemporal prompt for visual representation in 4D scene understanding. The spatiotemporal prompt is generated by encoding 3D position and 1D time into a dynamic-aware 4D coordinate embedding. Moreover, we demonstrate that spatial and temporal components disentangled from visual features are more effective in distinguishing the background from objects. This motivates embedding the 4D spatiotemporal prompt into these features to enhance the dynamic scene representation. By aligning visual spatiotemporal embeddings with language embeddings, LMMs gain the ability to understand both spatial and temporal characteristics of static background and dynamic objects in the physical world. Additionally, we construct a 4D vision-language dataset with spatiotemporal coordinate annotations for instruction fine-tuning LMMs. Extensive experiments have been conducted to demonstrate the superiority of our method on various tasks of 4D scene understanding. Our code: https://github.com/hyzhouboy/LLaVA-4D.

Zexi Fan, Yan Sun, Shihao Yang, Yiping Lu

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning (SCaSML), a framework that systematically improves pre-trained PDE solvers at inference time without any retraining. Our core idea is to derive a new PDE, which we term the Law of Defect, that precisely governs the error of a given surrogate model. Because this defect PDE retains the structure of the original problem, we can solve it efficiently with traditional stochastic simulators, yielding a targeted correction to the initial machine-learned solution. We prove that SCaSML achieves a faster convergence rate, with a final error bounded by the product of the surrogate and simulation errors. On challenging PDEs up to 160 dimensions, SCaSML reduces the error of various surrogate models, including PINNs and Gaussian Processes, by 20-80%. SCaSML provides a principled method to fuse the speed of machine learning with the rigor of numerical simulation, enhancing the trustworthiness of Al for scientific discovery.

Shenghe Zheng, Chenyu Huang, Fangchen Yu, Junchi Yao, Jingqi Ye, Tao Chen, Yun Luo, Ning Ding, LEI BAI, Ganqu Cui 等

As large language models (LLMs) are increasingly applied to scientific reasoning, the complexity of answer formats and the diversity of equivalent expressions make answer verification a critical yet challenging task. Existing verification studies in scientific domains suffer from two major limitations: (a) the absence of systematic evaluation standards and insufficient disciplinary coverage, which hinders their comprehensive assessment; and (b) heavy reliance on cumbersome rule design or prompt engineering, which reduces their effectiveness in complex reasoning scenarios or limits their cross-disciplinary generalization. To address these challenges, we propose solutions at both the data and model levels. On the data side, we construct **SCI-VerifyBench**, a cross-disciplinary benchmark covering mathematics, physics, biology, chemistry, and general scientific QA. The benchmark is built from real LLM responses and enhanced with domain-specific equivalence transformations that generate challenging and realistic data. Model-based and expert annotations ensure both quality and diversity, enabling rigorous evaluation of verification ability. On the model side, we emphasize the importance of reasoning for verification and introduce **SCI-Verifier**, a unified reasoning-augmented verifier for scientific domains. Through post-training, SCI-Verifier demonstrates strong logical reasoning and equivalence judgment capabilities while maintaining concise and stable outputs. Together, SCI-VerifyBench and SCI-Verifier provide a principled framework for scientific verification, offering both systematic evaluation and practical pathways to enhance the reliability and applicability of LLMs in scientific domains.

Computer Vision · Everything Else

Ye Lu, Jie Wang, Tianyi Liu, Jianjun Gao, Kim-Hui Yap

Stochastic Human Motion Prediction (HMP) has become an essential task for the realm of computer vision, for its capacity to anticipate accurate and diverse future human trajectories. Current diffusion-based techniques typically enforce skeletal consistency by encoding structural priors into network architectures. Although effective in promoting plausible kinematics, this approach provides only indirect control over the generative process and often fails to guarantee strict physical constraint satisfaction. In this work, we propose a structure-aligned and joint-aware diffusion framework that enforces physical constraints by embedding skeletal topology and joint-specific dynamics directly into the diffusion process. Specifically, our framework consists of two key modules, the Joint-Adaptive Noise Generator and the Structure-Aligned Constraint Enforcer. The former component, Joint-Adaptive Noise Generator, infers joint-specific dynamics and injects heterogeneous, instance-aware noise per joint and sample to capture spatial variability and enhance motion diversity. The latter component, Structure-Aligned Constraint Enforcer, encodes skeletal topology by modeling joint connectivity and bone lengths from historical motions, and it constrains each denoising step to preserve anatomical consistency. Through their synergistic operation, these modules grant KinemaDiff direct control over physical realism and motion diversity, addressing the common limitations of indirect structural priors and uniform noise application. Extensive experiments on multiple benchmarks demonstrate the effectiveness of our method, attributable to tailoring the diffusion process through structural alignment and joint-adaptive noise modeling.

Computer Vision · Vision Models & Multimodal

Guangyi Han, Wei Zhai, Yuhang Yang, Yang Cao, Zheng-Jun Zha

Hand-object interaction (HOI) is fundamental for humans to express intent. Existing HOI generation research is predominantly confined to fixed grasping patterns, where control is tied to physical priors such as force closure or generic intent instructions, even when expressed through elaborate language. Such an overly general conditioning imposes a strong inductive bias for stable grasps, thus failing to capture the diversity of daily HOI. To address these limitations, we introduce $\textbf{Free-Form HOI Generation}$, which aims to generate controllable, diverse, and physically plausible HOI conditioned on fine-grained intent, extending HOI from grasping to free-form interactions, like pushing, poking, and rotating. To support this task, we construct $\textbf{WildO2}$, an in-the-wild diverse 3D HOI dataset, which includes diverse HOI derived from internet videos. Specifically, it contains 4.4k unique interactions across 92 intents and 403 object categories, each with detailed semantic annotations. Building on this dataset, we propose $\textbf{TOUCH}$, a three-stage framework centered on a multi-level diffusion model that facilitates fine-grained semantic control to generate versatile hand poses beyond grasping priors. This process leverages explicit contact modeling for conditioning and is subsequently refined with contact consistency and physical constraints to ensure realism. Comprehensive experiments demonstrate our method's ability to generate controllable, diverse, and physically plausible hand interactions representative of daily activities.