mlsanityData to 14 Oct 2026

Pseudo-Hamiltonian neural networks for learning partial differential equations

arXiv 2304.14374 ↗First posted 27 Apr 2023cs.LG cs.NA math.NAcited by 10

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Abstract (arXiv)

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting model is comprised of up to three neural networks, modelling terms representing conservation, dissipation and external forces, and discrete convolution operators that can either be learned or be given as input. We demonstrate numerically the superior performance of PHNN compared to a baseline model that models the full dynamics by a single neural network. Moreover, since the PHNN model consists of three parts with different physical interpretations, these can be studied separately to gain insight into the system, and the learned model is applicable also if external forces are removed or changed.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 32 of its 69 references that are in the map. First posted on arXiv 27 Apr 2023.

Builds on

32 of 69 references.

References · 32

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20 more
  1. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 2; 2026: 4.

10 papers.

  1. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 7
  2. 2023Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulationscited by 3
  3. 2024Data-Driven Discovery of PDEs via the Adjoint Methodcited by 2
  4. 2025Neural non-canonical Hamiltonian dynamics for long-time simulationscited by 2
  5. 2026PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecastingcited by 2
  6. 2023Pseudo-Hamiltonian system identificationcited by 1
  7. 2026Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamicscited by 1
  8. 2024Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEscited by 0
  9. 2026Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physicscited by 0
  10. 2026Identifying the nonlinear string dynamics with port-Hamiltonian neural networkscited by 0