arXiv Machine Learning

MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

arXiv:2605. 13305v2 Announce Type: replace Abstract: Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons.

arXiv Machine Learning

Jul 1

Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics

arXiv:2601. 22123v4 Announce Type: replace Abstract: Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration.

By Winfried Ripken, Michael Plainer, Gregor Lied, Thorben Frank, Oliver T. Unke, Stefan Chmiela, Frank No\'e, Klaus-Robert M\"uller

arXiv Machine Learning

Jul 10

Neural non-canonical Hamiltonian dynamics for long-time simulations

arXiv:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.

By Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML)

arXiv Machine Learning

Jul 17

RTS Smoother-Guided Learning of Physics-Based Neural Differential Models

arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.

By Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba, Zachary D. Danziger, Deniz Erdogmus

benchmarks

arXiv Machine Learning

Aug 14

History-informed Lagrangian Neural Networks

arXiv:2608. 13215v1 Announce Type: new Abstract: Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously.

By Tianshuo Zhang, Xianglei Xing, Wenzhe Zhai, Jia Gao, He Cao

benchmarks

arXiv Machine Learning

Aug 14

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

arXiv Machine Learning

Jun 24

Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.

By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai

diffusion fine-tuning

arXiv AI

Aug 25

One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs

arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...

By Maqun Zhang, Feng Gao, Wankun Chen, Hui Yu, Yanhai Gan, Junyu Dong

agents benchmarks

arXiv Machine Learning

Jun 3

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.

By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu

diffusion safety

arXiv Machine Learning

Sep 10

Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

arXiv:2609.07814v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...

By Hanwen Wang, Paris Perdikaris

benchmarks

arXiv Machine Learning

Jun 9

Foundation Inference Models for Ordinary Differential Equations

arXiv:2602. 08733v2 Announce Type: replace Abstract: Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging.

By Maximilian Mauel, Johannes R. H\"ubers, David Berghaus, Patrick Seifner, Ramses J. Sanchez

fine-tuning

arXiv Machine Learning

Jun 26

Symplectic Neural Networks for learning Generalized Hamiltonians

arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas

arXiv AI

Jul 29

Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.

By Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer

rag benchmarks

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