mlsanityData to 14 Oct 2026

Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces

arXiv 2206.02660 ↗First posted 6 Jun 2022cs.LG cs.NA math.NAcited by 18

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Abstract (arXiv)

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a generalization of the Hamiltonian formulation via the port-Hamiltonian formulation, and show that pseudo-Hamiltonian neural network models can be used to learn external forces acting on a system. We argue that this property is particularly useful when the external forces are state dependent, in which case it is the pseudo-Hamiltonian structure that facilitates the separation of internal and external forces. Numerical results are provided for a forced and damped mass-spring system and a tank system of higher complexity, and a symmetric fourth-order integration scheme is introduced for improved training on sparse and noisy data.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 19 of its 40 references that are in the map. First posted on arXiv 6 Jun 2022.

Builds on

19 of 40 references.

References · 19

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Hamiltonian Neural Networkscited by 712
  3. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  4. 2019Symplectic Recurrent Neural Networkscited by 150
  5. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
  6. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 79
  7. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 67
  8. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  9. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 38
  10. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 38
  11. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  12. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
7 more
  1. 2020Sparse Symplectically Integrated Neural Networkscited by 20
  2. 2022Learning Hamiltonians of constrained mechanical systemscited by 14
  3. 2022Port-Hamiltonian Dynamic Mode Decompositioncited by 9
  4. 2020Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systemscited by 7
  5. 2020A Non-Intrusive Method to Inferring Linear Port-Hamiltonian Realizations using Time-Domain Datacited by 5
  6. 2018Robust port-Hamiltonian representations of passive systemscited by 4
  7. 2019Identification of Port-Hamiltonian Systems from Frequency Response Datacited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 3; 2025: 2; 2026: 5.

18 papers.

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  1. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  2. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 18
  3. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  4. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  5. 2022Thermodynamics of learning physical phenomenacited by 10
  6. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  7. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  8. 2023Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integratorscited by 4
  9. 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
  10. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  11. 2025Neural non-canonical Hamiltonian dynamics for long-time simulationscited by 2
  12. 2023Pseudo-Hamiltonian system identificationcited by 1
6 more
  1. 2024Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domainscited by 1
  2. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  3. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  4. 2026Structure- and Stability-Preserving Learning of Port-Hamiltonian Systemscited by 0
  5. 2026Learning partially observed systems with neural Hamiltonian ordinary differential equationscited by 0
  6. 2026Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reductioncited by 0