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Applications · Chemistry, Physics, and Earth Sciences

Karen Sargsyan, Chao-Ping Hsu

Finding exact solutions to the quantum many-body problem is computationally intractable (QMA-hard). Traditional approximations for electrons in an atom or molecule---density functional theory and wavefunction methods---have been indispensable, but their development shows signs of saturation: DFT functionals have proliferated without converging toward the exact functional, and strong correlation remains largely unsolved after decades of effort. This position paper argues that machine learning represents the most promising path forward---not as a proof of logical necessity, but as a decision-theoretic argument: ML succeeds whether the underlying problems are truly hard or merely lack simple analytical solutions. We reframe recent traditional method development as ``hand-crafted machine learning'' that has exhausted the hypothesis space accessible to human intuition. Significant challenges remain, but these have clear research paths forward, unlike the fundamental barriers facing traditional approaches. ML-based approaches merit strategic priority in quantum chemistry's next phase.

Applications · Chemistry, Physics, and Earth Sciences

Dario Coscia, Pim de Haan, Max Welling

Machine Learning Interatomic Potentials (MLIPs) are becoming a central tool in simulation-based chemistry. However, like most deep learning models, MLIPs struggle to make accurate predictions on out-of-distribution data or when trained in a data-scarce regime, both common scenarios in simulation-based chemistry. Moreover, MLIPs do not provide uncertainty estimates by construction, which are fundamental to guide active learning pipelines and to ensure the accuracy of simulation results compared to quantum calculations. To address this shortcoming, we propose BLIPs: Bayesian Learned Interatomic Potentials. BLIP is a scalable, architecture-agnostic variational Bayesian framework for training or fine-tuning MLIPs, built on an adaptive version of Variational Dropout. BLIP delivers well-calibrated uncertainty estimates and minimal computational overhead for energy and forces prediction at inference time, while integrating seamlessly with (equivariant) message-passing architectures. Empirical results on simulation-based computational chemistry tasks demonstrate improved predictive accuracy with respect to standard MLIPs, and trustworthy uncertainty estimates, especially in data-scarse or heavy out-of-distribution regimes. Moreover, fine-tuning pretrained MLIPs with BLIP yields consistent performance gains and calibrated uncertainties.

Applications · Chemistry, Physics, and Earth Sciences

Vincent Guan, Lazar Atanackovic, Kirill Neklyudov

The population dynamics of molecules, cells, and organisms are governed by a number of unknown internal and external forces. In the last decade, population dynamics have predominately been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering population dynamics that minimize Wasserstein Lagrangian action, rather than free energy. As our main theoretical contributions, we derive the Hamiltonian equations of motion from the principle of least population-level action and we show that these mechanics encompass classical mechanics, quantum mechanics, and gradient flows. We further leverage the Hamiltonian perspective to propose an algorithm that learns the population mechanics from observed marginals, without specifying the Lagrangian. We demonstrate that by directly learning the population mechanics, our method forecasts and interpolates unseen marginals without a reference process, and outperforms gradient flow and flow matching methods across a wide range of real and simulated experiments.

Deep Learning · Algorithms

Huayu Deng, Jinghui Zhong, Xiangming Zhu, Yunbo Wang, Xiaokang Yang

High-fidelity measurements of continuum physical fields are essential for scientific discovery and engineering design but remain challenging under sparse and constrained sensing. Conventional reconstruction methods typically rely on fixed sensor layouts, which cannot adapt to evolving physical states. We propose LASER, a unified, closed-loop framework that formulates active sensing as a Partially Observable Markov Decision Process (POMDP). At its core, LASER employs a continuum field latent world model that captures the underlying physical dynamics and provides intrinsic reward feedback. This enables a reinforcement learning policy to simulate ''what-if'' sensing scenarios within a latent imagination space. By conditioning sensor movements on predicted latent states, LASER navigates toward potentially high-information regions beyond current observations. Our experiments demonstrate that LASER consistently outperforms static and offline-optimized strategies, achieving high-fidelity reconstruction under sparsity across diverse continuum fields.

Applications · Chemistry, Physics, and Earth Sciences

Cheng Jing, Uvini Mudiyanselage, Woojin Cho, Minju Jo, Anthony Gruber, Kookjin Lee

Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative behavior. However, these models are typically trained on a per-configuration basis, requiring explicit knowledge of system parameters and costly retraining when these parameters vary. While meta-learning provides a potential remedy, optimization-based approaches can suffer from limited generalizability. Motivated by recent advances in modulation-based learning aimed at mitigating these drawbacks, we systematically investigate the use of modulation techniques in learning conservative dynamical systems. We study a range of existing modulation strategies alongside newly proposed variants, integrating them into a Hamiltonian learning framework without requiring an explicit system parameterization. Through extensive experiments on benchmark problems, we demonstrate that modulation-based meta-learning enables accurate few-shot adaptation, achieving robust generalization across parameter space without compromising the conservation of key invariants responsible for the dynamics.

Applications · Robotics

Haoyun Liu, Jianzhuang Zhao, Xinyuan Chang, Tianle Shi, Chuanzhang Meng, Jiayuan Tan, Feng Xiong, Tong Lin, Dongjie Huo, Mu Xu 等

Despite the rapid progress of Vision-Language-Action (VLA) models, the prevailing paradigm of predicting discrete waypoints remains fundamentally misaligned with the intrinsic continuity of physical motion. This discretization imposes rigid sampling rates, lacks high-order differentiability, and introduces quantization artifacts that hinder precise, compliant interaction. We propose Neural Implicit Action Fields (NIAF), a paradigm shift that reformulates action prediction from discrete waypoints to continuous action function regression. By utilizing an MLLM as a hierarchical spectral modulator over a learnable motion prior, NIAF synthesizes infinite-resolution trajectories as continuous-time manifolds. This formulation enables Analytical Differentiability, allowing for explicit supervision of velocity, acceleration, and jerk to ensure mathematical consistency and physical plausibility. Our approach achieves state-of-the-art results on CALVIN and LIBERO benchmarks across diverse backbones. Furthermore, real-world experiments demonstrate that NIAF enables stable impedance control, bridging the gap between high-level semantic understanding and low-level dynamic execution.

Applications · Chemistry, Physics, and Earth Sciences

Fengzhe Zhang, Laurence Midgley, Jose Miguel Hernandez-Lobato

Score-based diffusion models (SBDMs) are powerful amortized samplers for Boltzmann distributions; however, imperfect score estimates bias downstream Monte Carlo estimates. Classical importance sampling (IS) can correct this bias, but computing exact likelihoods requires solving the probability-flow ordinary differential equation (PF–ODE), a procedure that is prohibitively costly and scales poorly with dimensionality. We introduce Variance-Tuned Diffusion Importance Sampling (VT-DIS), a lightweight post-training method that adapts the per-step noise covariance of a pretrained SBDM by minimizing the $\alpha$-divergence $(\alpha=2)$ between its forward diffusion and reverse denoising trajectories. VT-DIS assigns a single trajectory-wise importance weight to the joint forward–reverse process, yielding unbiased expectation estimates at test time with negligible inference-time overhead compared to standard sampling. On the DW-4, LJ-13, and alanine-dipeptide benchmarks, VT-DIS achieves effective sample sizes of approximately 80%, 35%, and 3.5%, respectively, while using only a fraction of the computational budget required by vanilla diffusion + IS or PF-ODE–based IS.

Reinforcement Learning · Everything Else

Xiangming Zhu, Huayu Deng, Haoran Zhao, Yiwei Hao, Yunbo Wang

Learning humanoid control from video provides a scalable alternative to the scarcity of high-fidelity robot data. Existing methods, however, often rely on curated datasets and treat video as passive kinematic priors. They fail to capture dynamic humanoid interactions with the environment, which are essential for real-world deployment. To address this, we propose TRansferable Interaction Primitives (TRIP), a framework designed to extract and ground interactions from unstructured, unlabeled game videos for physical controllers. TRIP explicitly models dependencies between motion dynamics and environmental context via a discrete library of interaction-based action primitives. To bridge the reality gap, we introduce a shared context latent space that aligns implicit video-domain features with functional target-domain observations, enabling the seamless transfer of video-mined strategies to reinforcement learning policies. Our experiments on complex terrain navigation demonstrate that TRIP achieves significant improvements in task performance, sample efficiency, and robustness.

Hao Wang, Shiqi Wang, Qi Liu

Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical constraints. Existing methods excel at semantic alignment, however, they struggle to maintain precise object contact. We reveal a key finding termed $\textit{Geometric Forgetting}$: as diffusion model depth increases, semantic feature tend to overshadow object geometry feature, causing the model to lose its perception to object geometry. To address this, we propose MaMi-HOI, a hierarchical framework reconciling Macro-level kinematic fluidity with Micro-level spatial precision. First, to counteract geometric forgetting, we introduce the Geometry-Aware Proximity Adapter (GAPA), which explicitly re-injects dense object details to perform residual snapping corrections for precise contact. Nevertheless, such aggressive local enforcement can disrupt global dynamics, leading to robotic stiffness. In response, we introduce the Kinematic Harmony Adapter (KHA), which proactively aligns whole-body posture with spatial objectives, ensuring the skeleton actively accommodates constraints without compromising naturalness. Extensive experiments validate that MaMi-HOI simultaneously achieves natural motion and precise contact. Crucially, it extends generation capabilities to long-term tasks with complex trajectories, effectively bridging the gap between global navigation and high-fidelity manipulation in 3D scenes.

Applications · Robotics

Zhiming Xu, Weitao Zhou, Xianghui Pan, Chenpeng Yao, Nanshan Deng, Chengju Liu, Qijun Chen

Real-world dynamics shifts pose a critical challenge for reinforcement learning, yet prior methods typically rely on encoding explicitly identified physical parameters into a latent context, a rigid parameterization that proves brittle to unmodeled or compound dynamics variations. We instead investigate dynamics adaptation through the lens of latent geometry, and show theoretically that target-domain regret is controlled by the Lipschitz smoothness of a trajectory dynamics encoder. We further prove that this Lipschitz constant can be upper-bounded through optimizing a multi-positive InfoNCE objective, yielding a smooth, task-relevant latent topology without privileged dynamics information. On MuJoCo benchmarks, our method significantly outperforms explicit identification baselines under severe dynamics shifts, including unmodeled structural failures, while simultaneously improving in-distribution stability and latent interpretability. Overall, these results validate that controlling latent smoothness is a principled and scalable mechanism for robust adaptation.

Applications · Time Series

YingHao Ai, Yukai Zhou, Ruoxi Jiang, Junyi An, Chao Qu, Zhijian Zhou, Shiyu Wang, Fenglei Cao, Zenglin Xu, Furao Shen 等

Spatio-temporal forecasting is critical for real-world applications like traffic management, yet capturing complex interactions under high-noise conditions remains challenging. While current methods have shown improved accuracy using spatial physical priors, they often struggle with evolving temporal correlations and systematic errors. In this work, we propose a nested forecasting framework that couples future macro-level regional trends with micro-level historical observations, enabling top-down guidance from abstract future representations for fine-grained forecasting. Specifically, we construct semantically coherent regions via spectral clustering and design a progressive coarse-to-fine predictor to inject macro-dynamics into node-level forecasting. Extensive experiments on multiple real-world datasets demonstrate that our method consistently outperforms state-of-the-art baselines, validating the effectiveness of future macro-guided nested forecasting.

Deep Learning · Graph Neural Networks

Xuan Minh Vuong Nguyen, Nissrine Akkari, Fabien Casenave, Jonathan Viquerat, Elie Hachem

Graph Neural Networks (GNNs) on meshes have emerged as promising surrogates for computational mechanics, but standard local message passing struggles to propagate information across unstructured meshes, leading to large errors in regions with complex physics (e.g., shocks, wakes, boundary layers). Existing approaches enlarge connectivity with long-range edges chosen *a priori* via geometric heuristics or random sampling, which lack a mechanism to prioritize high-error regions and often introduce redundant communication. We propose **MiSe-GNN**, a dual-head architecture that adaptively augments graph connectivity using model-predicted *a posteriori* errors. MiSe-GNN jointly predicts physical fields and a node-wise error indicator; the predicted error is periodically converted into a hierarchy of additional edges via an adaptive tree that links high-error nodes to spatial pivots at multiple scales. This error-guided connectivity concentrates message passing where the surrogate is uncertain while keeping the graph sparse elsewhere, yielding a transparent and physically interpretable graph-space analogue of adaptive mesh refinement. Across industrial CFD and CSD benchmarks, MiSe-GNN consistently improves accuracy and accuracy–compute trade-offs over strong baselines, and qualitative analyses show that it routes communication toward physically challenging regions. These results establish *error-guided edge augmentation* as a robust and general design principle for long-range message passing in physics-aware GNNs.

Applications · Chemistry, Physics, and Earth Sciences

Jaemin Seo, Su Rin Lee, JaeYong Lee

Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler–Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods.

Deep Learning · Everything Else

Sisi Dai, Xinxin Su, Kai Xu

Large-scale, high-quality dynamic 3D (4D) assets are essential for learning physically grounded representations, but remain costly to capture and annotate at scale. This limits the viability of supervised 4D learning and motivates zero-shot text-to-4D generation leveraging pretrained diffusion priors. To model complex dynamics, prior methods typically adopt implicit 3D representations (e.g., NeRFs or 3DGS) for their deformation capacity. However, their implicit nature provides limited control over surface topology, which hinders high-fidelity geometry and makes temporally coherent surface reconstruction challenging. To address these limitations, we explore zero-shot text-to-4D mesh generation. However, a structural mismatch arises when combining diffusion-based guidance with topology-constrained meshes: the guidance is noisy and spatially inconsistent, while meshes impose severe topological constraints, making direct vertex-level deformation unstable. In this paper, we introduce TextMesh4D, the first zero-shot framework for text-to-4D that directly generates dynamic meshes by addressing the above challenge at two complementary levels. Geometrically, we shift deformation modeling from vertices to faces via a Jacobian Deformation Field (JDF), enabling topology-aware surface reconstruction through an integrability-enforcing integration formulation. Semantically, we propose a Local-Global Semantic Regularizer (LGSR) that preserves identity over time by jointly constraining local deformation plausibility and global shape consistency. Extensive experiments demonstrate state-of-the-art temporal consistency, structural fidelity, and visual quality, while remaining efficient on a single 24GB GPU. The code will be released to facilitate future research.

Applications · Chemistry, Physics, and Earth Sciences

Minkyu Kim, Nayoung Kim, Honghui Kim, Sungsoo Ahn

Discovering heterogeneous catalysts tailored for specific reaction intermediates remains a fundamental bottleneck in materials science. While traditional trial-and-error methods and recent generative models have shown promise, they struggle to capture the intrinsic coupling between surface geometry and adsorbate interactions. To address this limitation, we propose CatFlow, a flow matching-based framework for de novo design and structure prediction of heterogeneous catalysts. Our model operates on a primitive cell-based factorized representation of the slab-adsorbate complex, reducing the number of learnable variables by an average of 9.2x while explicitly encoding the surface orientation of the slab-adsorbate interface. Experiments on the Open Catalyst 2020 dataset demonstrate that CatFlow significantly improves the structural fidelity of generated catalysts compared to autoregressive and sequential baselines. Further experiments show that the generated structures accurately capture the adsorption energy distributions of physically plausible interfaces and lie closer to thermodynamic local minima.

Applications · Robotics

Guanhua Ji, Harsha Polavaram, Lawrence Yunliang Chen, Sandeep Bajamahal, Zehan Ma, Simeon Adebola, Chenfeng Xu, Ken Goldberg

Large and diverse datasets are needed for training generalist robot policies that have potential to control a variety of robot embodiments--robot arm and gripper combinations--across diverse tasks and environments. As re-collecting demonstrations and retraining for each new hardware platform are prohibitively costly, we show that existing robot data can be augmented for transfer and generalization. The Open X-Embodiment (OXE) dataset, which aggregates demonstrations from over 60 robot datasets, has been widely used as the foundation for training generalist policies. However, it is highly imbalanced: the top four robot types account for over 85% of its real data, which risks overfitting to robot--scene combinations. We present AugE-Toolkit, a scalable robot augmentation pipeline, and OXE-AugE, a high-quality open-source dataset that augments OXE with 9 different robot embodiments. OXE-AugE provides over 4.4 million trajectories, more than triple the size of the original OXE. We conduct a systematic study of how scaling robot augmentation impacts cross-embodiment learning. Results suggest that augmenting datasets with diverse arms and grippers improves policy performance not only on the augmented robots, but also on unseen robots and even the original robots under distribution shifts. In physical experiments, we demonstrate that generalist policies such as OpenVLA and $\pi_0$ benefit from fine-tuning on OXE-AugE, improving success rates by 24-45% on previously unseen robot-gripper combinations across four real-world manipulation tasks.

Applications · Chemistry, Physics, and Earth Sciences

Guoze Sun, Tianya Miao, Haoyang Huang, Huaguan Chen, Han Wan, Rui Zhang, Hao Sun

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (GANO), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. GANO encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-injected surrogate provides a reliable gradient pathway for geometry updates. Moreover, GANO supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to $+55.9\%$ lift-to-drag improvement for airfoils and $\sim 7\%$ drag reduction for vehicles.

Applications · Health / Medicine

Ziyang Liu, Ruiqiang Xiao, Chang Huang, KIEREN YU, Siyuan He, Kaishun WU

Continuous ECG monitoring is clinically valuable, but scaling it beyond electrodes to comfortable long-term use motivates contactless mmWave sensing. In practice, mmWave-to-ECG reconstruction is severely constrained by the scarcity of high-quality synchronized recordings and poor cross-subject generalization. To overcome these bottlenecks, we propose \textbf{Cardio-mmFlow}, a Gaussian-prior-free physics-informed flow matching framework that synthesizes realistic mmWave radar signals from abundant clinical ECG corpora. It learns a direct transport trajectory between the latent manifolds of ECG and radar. To capture subject-dependent propagation differences, we incorporate a simplified mass--spring--damper inspired physical prior and inject it into the flow dynamics via feature-wise linear modulation for personalization. Extensive experiments show that our system have generate high fidelity radar data in both signal and latent domains. It significantly improve zero-shot downstream mmWave$\rightarrow$ECG task, and enable Atrial Fibrillation classification with synthetic data. Further analysis evaluate the model interpretability.

Deep Learning · Large Language Models

Xiyuan Zhou, Ruixi Zou, Xinlei Wang, Yuheng Cheng, Yan Xu, Junhua Zhao, Jinjin Gu

Engineering problem solving is central to real-world decision-making, requiring mathematical formulations that not only represent complex problems but also produce feasible solutions under data and physical constraints. Unlike mathematical problem solving, which operates on predefined formulations, engineering tasks demand open-ended analysis, feasibility-driven modeling, and iterative refinement. Although large language models (LLMs) have shown strong capabilities in reasoning and code generation, they often fail to ensure feasibility, which limits their applicability to engineering problem solving. To address this challenge, we propose EngiAgent, a multi-agent system with a fully connected coordinator that simulates expert workflows through specialized agents for problem analysis, modeling, verification, solving, and solution evaluation. The fully connected coordinator enables flexible feedback routing, overcoming the rigidity of prior pipeline-based reflection methods and ensuring feasibility at every stage of the process. This design not only improves robustness to diverse failure cases such as data extraction errors, constraint inconsistencies, and solver failures, but also enhances the overall quality of problem solving. Empirical results across four representative domains demonstrate that EngiAgent achieves substantial improvements in feasibility compared to prior approaches, establishing a new paradigm for feasibility-oriented engineering problem solving with LLMs. Our source code and data are available at https://anonymous.4open.science/r/EngiAgent-1C8A.

Applications · Chemistry, Physics, and Earth Sciences

Pietro Sittoni, Emanuele Zangrando, Angelo Alberto Casulli, Nicola Guglielmi, Francesco Tudisco

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs associated with generating large-scale, high-quality datasets and training models. In this work, inspired by studies on the structure of Green's functions for elliptic PDEs, we introduce Neural-HSS, a parameter-efficient architecture built upon the Hierarchical Semi-Separable (HSS) matrix structure that is provably data-efficient for a broad class of PDEs. We theoretically analyze the proposed architecture, proving that it satisfies exactness properties even in very low-data regimes. We also investigate its connections with other architectural primitives, such as the Fourier neural operator layer and convolutional layers. We experimentally validate the data efficiency of Neural-HSS on the three-dimensional Poisson equation over a grid of two million points, demonstrating its superior ability to learn from data generated by elliptic PDEs in the low-data regime while outperforming baseline methods. Finally, we demonstrate its capability to learn from data arising from a broad class of PDEs in diverse domains, including electromagnetism, fluid dynamics, and biology.