Hamiltonian Neural Networks

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Hamiltonian Neural Networks (HNNs) learn a system’s energy function and derive its evolution from Hamilton’s equations, aiming to preserve physical structure rather than fit trajectories alone. Common approaches pair neural energy models with symplectic integrators, latent or separable representations, and port-Hamiltonian formulations that handle forcing, dissipation, or noise; extensions also address partially observed systems and partial differential equations. These models support system identification and long-horizon forecasting in settings such as oscillators, celestial mechanics, and physical world models. A central tension is that structural constraints can improve energy conservation without guaranteeing accurate chaotic trajectories or phase-space geometry, while sparse data and gauge freedom can make the learned Hamiltonian difficult to identify.

Latest papers

30 papers2 papers in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do
Oct 18, 2026Andrew Qing HeStructure-Preserving Neural Networks Hamiltonian Neural Networks
Duke University
Lagrangian--Hamiltonian Flows for Video Prediction and Image Generation: A Symplectic Perspective
Sep 28, 2026Jiawei HuImage Generation Hamiltonian Neural Networks
Department of Mathematics and Statistics, Boston University
Lagrangian and Hamiltonian Neural Networks With a Dissipative System
Sep 25, 2026V. Rayamajhi, J. SingalLagrangian Neural Networks Hamiltonian Neural Networks
University of Richmond
Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physics
Sep 24, 2026Yufeng Wang, Parivesh Priye, Lu Wei +1World Model Learning Physics-Informed ML
Stony Brook University · Georgia Institute of Technology · Westlake University
Riemannian Neural Hamiltonian Flows: Geodesic Symplectic Transport and Interpretability
Sep 18, 2026Vincent SouvetonNormalizing Flows Hamiltonian Dynamics
CEA, DAM, DIF, Arpajon, F-91297, France
Continuous Learning of Gravity Field Irregularities Around Small Bodies via Neural Hamiltonian ODEs
Sep 10, 2026Giacomo Acciarini, Dario IzzoDynamical Systems Hamiltonian Neural Networks
Advanced Concepts Team, European Space Agency, ESTEC, Noordwijk, The Netherlands
Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration
Sep 3, 2026Lidia J. Gomes Da SilvaDynamical Systems Gravitational-Wave Astronomy
SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN Sezione di Trieste · INFN Sezione di Trieste · IFPU - Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
Latent unified smooth Hamiltonians for excited state chemistry
Sep 1, 2026David Juergens, Martin Stöhr, Andreas E. Hillers-Bendtsen +2Implicit Neural Representations Quantum Chemistry
Department of Chemistry and The PULSE Institute, Stanford University, Stanford 4305, California, USA · SLAC National Accelerator Laboratory, Menlo Park, 94025, California, USA
Learning Deterministic and Stochastic Forced Hamiltonian Systems
Aug 20, 2026Benedikt Brantner, Tomasz TyranowskiStructure-Preserving Neural Networks Hamiltonian 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
A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics
Aug 10, 2026Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim TeweDynamical Systems Hamiltonian Neural Networks
African Institute for Mathematical Sciences (AIMS) Senegal
Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks
Jul 31, 2026Jaesung ChoiNeural Surrogate Modeling Dynamical Systems
Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics
Jul 31, 2026Vakhtang PutkaradzeLatent Dynamics Modeling Hamiltonian Neural Networks
Department of Mathematics, The University of Alabama, Gordon Palmer Hall, Tuscaloosa, AL, 35401, USA
Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
Jul 14, 2026Dibakar SigdelHamiltonian Neural Networks Port-Hamiltonian Systems
1Mindverse Computing LLC, Lynnwood, WA 98087
The Equilibrium Is the Initialization: Lazy Identity Collapse in Physics-Structured Deep Equilibrium Reasoning
Jul 13, 2026Joyjeet SinghDynamical Systems Hamiltonian Neural Networks
Independent Researcher
Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models
Jul 8, 2026Eli Laird, Corey ClarkPhysical Consistency in Video Generation Latent Dynamics Modeling
Department of Computer Science, Southern Methodist University, Dallas, TX, USA
Symplectic Neural Networks for learning Generalized Hamiltonians
Jun 25, 2026Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta +2Dynamical Systems Symplectic RNNs
Computer Science Department, Indraprasth Institute of Information Technology, New Delhi, India 110020 · Athena Research and Innovation Center, Marousi, Greece 15125 · HSBC Holdings, Singapore
Learning partially observed systems with neural Hamiltonian ordinary differential equations
May 22, 2026Sunniva Meltzer, Sølve Eidnes, Alexander Johannes StasikDynamical Systems Latent 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
Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
May 20, 2026Jack KendallEquilibrium Propagation Dynamical Systems
Zyphra · San Francisco, CA
Identifying the nonlinear string dynamics with port-Hamiltonian neural networks
May 12, 2026Maximino Linares, Guillaume Doras, Thomas HélieDynamical Systems Nonlinear System Identification
1IRCAM, 1, place Igor-Stravinsky, 75004, Paris, France · 2Sorbonne Université, 4, place Jussieu, 75005, Paris, France · 3CNRS, 3 rue Michel-Ange, 75016, Paris, France
HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planning
May 7, 2026Haoyun Tang, Haodong Cui, Keyao Xu +2World Model Learning Latent Dynamics Modeling
1Xi’an Jiaotong University · 2Huazhong University of Science and Technology · 3Nankai University +1
Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data
Apr 19, 2026Vedanta Thapar, Abhinav GuptaNonlinear System Identification Recurrent Neural Networks
The Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom · Center for Theoretical Physics, St. Stephen’s College, University of Delhi, Delhi 110007, India
Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems
Apr 14, 2026Binh Nguyen, Nam T. Nguyen, Truong X. NghiemPort-Hamiltonian Systems Hamiltonian Neural Networks
Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach
Apr 1, 2026Abrari Noor Hasmi, Haralampos Hatzikirou, Hadi SusantoSymplectic RNNs Hamiltonian Neural Networks
Department of Mathematics, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates · Public Health and Epidemeology Department, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates.
A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks
Mar 26, 2026Guojie Li, Liu HongPhysics-Informed ML PDE Inverse Problems
School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China.
Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees
Mar 10, 2026Luca Di Persio, Matthias Ehrhardt, Youness OutalebPort-Hamiltonian Systems Hamiltonian Neural Networks
Department of Computer Science - College of Mathematics University of Verona, Strada le Grazie 15 - 37134 Verona, Italy · University of Wuppertal, Chair of Applied and Computational Mathematics, Gaußstrasse 20, 42119 Wuppertal, Germany · Doctoral School in Mathematics, University of Trento Via Sommarive, 14 - 38123 Povo, Italy
Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics
Mar 6, 2026Yaojun Li, Yulong Yang, Christine Allen-BlanchetteHamiltonian Neural Networks Dynamical Systems
Princeton University, USA
CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning
Mar 2, 2026Pratik Jawahar, Maurizio PieriniSymplectic RNNs Hamiltonian Neural Networks
University of Manchester · CERN
Deepmechanics
Feb 20, 2026Abhay Shinde, Aryan Amit Barsainyan, Jose Siguenza +3Symplectic RNNs Lagrangian Neural Networks
Deep Forest Sciences, Mumbai, Maharashtra, India · Deep Forest Sciences, Bengaluru, Karnataka, India · Deep Forest Sciences, Palo alto, California, USA +1
PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting
Feb 20, 2026Shubham Bhardwaj, Chandrajit BajajTime Series Forecasting Port-Hamiltonian Systems
Department of Computer Science, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA
Neural non-canonical Hamiltonian dynamics for long-time simulations
Oct 2, 2025Clémentine Courtès, Emmanuel Franck, Michael Kraus +2Dynamical Systems Nonlinear System Identification
IRMA, MACARON · Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, 7 rue René Descartes 672000 Strasbourg, France. · INRIA Nancy-Grand Est, MACARON Project, Strasbourg, France. +5

Oct 18, 2026J/K move · Enter open · S save

Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do

Andrew Qing He

Duke University

Structure-Preserving Neural Networks Hamiltonian Neural Networks Dynamical Systems

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Exactly symplectic neural networks are built almost exclusively from shear maps and gain expressivity only through depth. We ask what else a single explicit symplectic layer can be. Observing that every layer in use is the exact flow of a Hamiltonian that is a function of commuting integrals, we obtain three families of layers: a learned-type layer, in which every conjugate pair is rotated, squeezed or sheared by a state-dependent amount and the type is found by training; moving-plane shears, residual symplectic maps outside the known ridge-function class; and fiber-preserving layers, which combine an unconstrained point transformation with a fiber translation at the cost of one linear solve. We characterize residual symplectic layers

x \mapsto x + J\nabla H(x)

: in one degree of freedom they are exactly the shears along a line, while from two degrees of freedom on a strictly larger class exists. Conjugating a learned-type layer by a symplectic network yields an exact one-parameter group with an exactly conserved learned Hamiltonian. In experiments on sixteen systems with one to forty degrees of freedom, against SympNets, HénonNets and learned-plane shear networks, layers built on nonlinear integrals are far more accurate when the Hamiltonian contains functions of those integrals. On nonlinear Schrödinger lattices with six to forty sites, twist layers alternating with linear symplectic maps are over a hundred times more accurate than every shear-based network, and with an on-site potential of learned form three to four orders of magnitude more accurate. On chains of Tao oscillators with the step size as an input, stretch layers are 45 to 70 times more accurate than learned-plane shears and recover the Hamiltonian to 1%. On generic non-separable systems, fiber layers improve on learned-plane shears by at most a factor of two, and widening the networks does not help any architecture.