arXiv Machine Learning July 7, 2026 By Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Serafim Kalliadasis

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

Read the original on arXiv Machine 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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

benchmarks

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

5d ago

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

5d ago

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

Related stories

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

Neural non-canonical Hamiltonian dynamics for long-time simulations

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

History-informed Lagrangian Neural Networks

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training