mlsanityData to 7 Oct 2026

Hamiltonian neural networks for solving equations of motion

arXiv 2001.11107 ↗First posted 29 Jan 2020physics.comp-ph cs.LGcited by 33

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Abstract (arXiv)

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Henon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network in order to achieve the same order of the numerical error in the predicted phase space trajectories.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jan 2020.

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Citing papers per year: 2021: 1; 2022: 8; 2023: 5; 2024: 6; 2025: 10; 2026: 3.

33 papers.

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  1. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  2. 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
  3. 2022Thermodynamics of learning physical phenomenacited by 10
  4. 2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
  5. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  6. 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
  7. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  8. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  9. 2025Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraintscited by 4
  10. 2022RcTorch: a PyTorch Reservoir Computing Package with Automated Hyper-Parameter Optimizationcited by 3
  11. 2024Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflationcited by 3
  12. 2022Bayesian Inference with Latent Hamiltonian Neural Networkscited by 2
21 more
  1. 2022First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfacescited by 2
  2. 2025Physically Plausible Multi-System Trajectory Generation and Symmetry Discoverycited by 2
  3. 2022Enhancing Neural Network Differential Equation Solverscited by 1
  4. 2023Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Mediacited by 1
  5. 2023Iterative Magnitude Pruning as a Renormalisation Group: A Study in The Context of The Lottery Ticket Hypothesiscited by 1
  6. 2023Separable Hamiltonian Neural Networkscited by 1
  7. 2024Lagrangian neural networks for nonholonomic mechanicscited by 1
  8. 2025Hamiltonian Neural Networks approach to fuzzball geodesicscited by 1
  9. 2025Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structurescited by 1
  10. 2025Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flowscited by 1
  11. 2026Symmetry-Constrained Language-Guided Program Synthesis for Discovering Governing Equations from Noisy and Partial Observationscited by 1
  12. 2022Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inferencecited by 0
  13. 2022Optimization-Informed Neural Networkscited by 0
  14. 2023Transferability of Winning Lottery Tickets in Neural Network Differential Equation Solverscited by 0
  15. 2024Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical responsecited by 0
  16. 2024GradINN: Gradient Informed Neural Networkcited by 0
  17. 2025UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flowscited by 0
  18. 2025Hamiltonian Neural PDE Solvers through Functional Approximationcited by 0
  19. 2025Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithmcited by 0
  20. 2026Gravitational Duals from Equations of State II: Large Hierarchies and False Vacuacited by 0
  21. 2026Physics-Informed Neural Embeddings of PDE Solution Familiescited by 0