Hamiltonian Dynamics

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Overview

Hamiltonian dynamics describes how positions and momenta evolve under an energy function, providing a framework for mechanics, molecular motion, and wave equations. Researchers use symplectic integrators and learned models such as Hamiltonian neural networks, symplectic neural operators, and port-Hamiltonian networks to preserve energy or account for forcing and dissipation. These methods support long-time simulation, system identification, dimensionality reduction, and planning in learned world models. A central challenge is that preserving energy or symplectic structure does not by itself guarantee accurate trajectories, phase-space topology, or generalization, especially with partial observations, dissipation, and learned coordinates.

Latest papers

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43 papers3 papers in the last four weeks, down 25% on the four weeks before. 0.0% of all new papers.

  1. LeHami: Symplectic Latent Dynamics for World Models

    Oct 11, 2026Romina Yalovetzky, Randall Balestriero, Yann LeCunLatent Dynamics ModelingLatent World Models

    Courant Institute, New York University · Brown University · AMI Labs

  2. Out-of-control Hamiltonian Learning

    Oct 5, 2026Weiyuan Gong, Muzhou Ma, Sitan Chen +2Quantum Many-Body PhysicsHamiltonian Dynamics

    Harvard University. · Caltech. · Oratomic.

  3. Nonlocal Hamiltonian Dynamics on Sparse Lévy Graphs: Spectral Analysis and Multimodal Sampling

    Oct 1, 2026Miaolei Zheng, Ting Gao, Jinqiao DuanHamiltonian DynamicsOptimal Transport

    School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China · School of Sciences, Great Bay University, Dongguan 523000, China · Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems, Great Bay University, Dongguan 523000, China +3

  4. HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps

    Sep 26, 2026Haoxiang Huang, Xiang Liu, Shuwei Wang +2Physics-Informed Diffusion ModelsDynamical Systems

    University of Science and Technology of China · Tsinghua University · Chinese Academy of Sciences

  5. Lagrangian and Hamiltonian Neural Networks With a Dissipative System

    Sep 25, 2026V. Rayamajhi, J. SingalLagrangian Neural NetworksHamiltonian Neural Networks

    University of Richmond

  6. Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs

    Sep 24, 2026Teo Deveney, Baige Xu, Takaharu YaguchiPDE Operator LearningNeural Operators

    Department of Computer Science, University of Bath, United Kingdom · Center for Advanced Intelligence Project, RIKEN, Japan · Kyushu University / Center for Advanced Intelligence Project, RIKEN, Japan

  7. Riemannian Neural Hamiltonian Flows: Geodesic Symplectic Transport and Interpretability

    Sep 18, 2026Vincent SouvetonNormalizing FlowsHamiltonian Dynamics

    CEA, DAM, DIF, Arpajon, F-91297, France

  8. MOSH-WM: Mask-Grounded Soft-Hamiltonian Dynamics for Object-Centric World Models

    Aug 24, 2026Zhekai Wang, Haoxiang Huang, Xiang Liu +6Object-Centric World ModelsVideo World Models

    Beijing Institute of Technology · University of Science and Technology of China · Tsinghua University +1

  9. Learning Deterministic and Stochastic Forced Hamiltonian Systems

    Aug 20, 2026Benedikt Brantner, Tomasz TyranowskiStructure-Preserving Neural NetworksHamiltonian Neural Networks

    Max-Planck-Institut für Plasmaphysik Boltzmannstraße 2, 85748 Garching, Germany · Technische Universität München, Zentrum Mathematik Boltzmannstraße 3, 85748 Garching, Germany · University of Twente, Department of Applied Mathematics PO Box 217, 7500AE Enschede, The Netherlands

  10. A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

    Aug 10, 2026Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim TeweDynamical SystemsHamiltonian Neural Networks

    African Institute for Mathematical Sciences (AIMS) Senegal

  11. Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks

    Jul 31, 2026Jaesung ChoiNeural Surrogate ModelingDynamical Systems

    Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

  12. Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

    Jul 31, 2026Vakhtang PutkaradzeLatent Dynamics ModelingHamiltonian Neural Networks

    Department of Mathematics, The University of Alabama, Gordon Palmer Hall, Tuscaloosa, AL, 35401, USA

  13. When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization

    Jul 26, 2026George A KevrekidisOptimization Convergence AnalysisHamiltonian Dynamics

    Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA

  14. Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics

    Jul 22, 2026Abhishek ShankarResidual LearningHamiltonian Dynamics

  15. Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity

    Jul 14, 2026Dibakar SigdelHamiltonian Neural NetworksPort-Hamiltonian Systems

    1Mindverse Computing LLC, Lynnwood, WA 98087

  16. Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models

    Jul 8, 2026Eli Laird, Corey ClarkPhysical Consistency in Video GenerationLatent Dynamics Modeling

    Department of Computer Science, Southern Methodist University, Dallas, TX, USA

  17. CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems

    Jul 3, 2026Jiale Gong, Pengzhan Jin, Dongyang Kuang +2Dynamical SystemsNonlinear System Identification

    School of Mathematics · School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China · National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China +3

  18. Compositional Dynamics in Learning and Mechanics

    Jun 27, 2026David I. SpivakDynamical SystemsHamiltonian Dynamics

  19. Symplectic Neural Networks for learning Generalized Hamiltonians

    Jun 25, 2026Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta +2Dynamical SystemsSymplectic RNNs

    Computer Science Department, Indraprasth Institute of Information Technology, New Delhi, India 110020 · Athena Research and Innovation Center, Marousi, Greece 15125 · HSBC Holdings, Singapore

  20. When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models

    Jun 23, 2026Hongbo WangDynamical SystemsLatent World Models

    Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA

  21. Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time

    Jun 15, 2026Xiuyuan Wang, Vishwak Srinivasan, Qiang Fu +3Hamiltonian Dynamics

    Department of Computer Science, Yale University · Department of EECS, Massachusetts Institute of Technology

  22. Learning symplectic model reduction based on a approximation theorem of symplectic embeddings

    Jun 3, 2026Liyi Feng, Yifa Tang, Yulin Xie +2Dynamical SystemsAutoencoders

    School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China · Department of Mathematics, National University of Singapore, 119076, Singapore

  23. Learning partially observed systems with neural Hamiltonian ordinary differential equations

    May 22, 2026Sunniva Meltzer, Sølve Eidnes, Alexander Johannes StasikDynamical SystemsLatent Dynamics Modeling

    Department of Mathematics and Cybernetics, SINTEF Digital, Norway · Department of Physics, University of Oslo, Norway · Department of Data Science, Norwegian University of Life Science, Norway

  24. Beyond Isotropy in JEPAs: Hamiltonian Geometry and Symplectic Prediction

    May 19, 2026Robert Jenkinson AlvarezJoint-Embedding Predictive ArchitectureGeometric Representation Learning

  25. PH-Dreamer: A Physics-Driven World Model via Port-Hamiltonian Generative Dynamics

    May 18, 2026Xueyu Luan, Chenwei ShiDynamical SystemsReinforcement Learning

    School of Electronic and Information Engineering Tongji University Shanghai 200092, China · Shanghai Research Institute for Intelligent Autonomous Systems Tongji University Shanghai 200092, China

  26. Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators

    May 16, 2026Andrew Bukowski, Aditya Kothari, Simba Shi +1Neural Surrogate ModelingDynamical Systems

    Yale University

  27. Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure

    May 15, 2026Peilun Li, Kaiyuan Tan, Daniel Moyer +1Contrastive LearningLatent Dynamics Modeling

    Department of Computer Science Vanderbilt University Nashville, TN 37235

  28. Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

    May 15, 2026Yeang Makara, Yusuke Tanaka, Takashi Matsubara +1PDE Operator LearningNeural Operators

    Graduate School of Science Kobe University 1-1 Rokkodai-cho, Nada-ku, Kobe, Japan · NTT Communication Science Laboratories 2-4, Hikaridai, Seika-cho, Soraku-gun, Kyoto, Japan · Faculty of Information Science and Technology Hokkaido University Kita 14, Nishi 9, Kita-ku, Sapporo, Hokkaido, Japan +1

  29. Physics Guided Generative Optimization for Trotter Suzuki Decomposition

    May 13, 2026WenBin YanQuantum Circuit OptimizationQuantum Circuit Compilation

    University of Colorado Boulder[quant-ph]

  30. When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize

    May 7, 2026Yi Wang, Chandrajit BajajDynamical SystemsLearning to Optimize

    1Oden Institute · Department of Computer Science