Pseudo-Hamiltonian neural networks for learning partial differential equations

Sølve Eidnes, Kjetil Olsen Lye
4/27/2023
cs.LGmath.NA

No official code found. Best implementation: SINTEF/pseudo-hamiltonian-neural-networks (19 stars, MIT, last commit 2025-03-12).

Abstract

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.

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Code Implementations(1)

SINTEF/pseudo-hamiltonian-neural-networksCommunity100%
MIT

The package phlearn for modelling pseudo-Hamiltonian systems by pseudo-Hamiltonian neural networks (PHNN), for ODEs and PDEs

193Python, MakefileAug 3, 20221 years agoMIT
dynamical-systemshamiltonian-dynamicsneural-networkordinary-differential-equationspartial-differential-equations+2 more

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Cite this paper

@article{eidnes2023pseudohamiltonian,
  title  = {Pseudo-Hamiltonian neural networks for learning partial differential equations},
  author = {Sølve Eidnes and Kjetil Olsen Lye},
  year   = {2023},
  eprint = {2304.14374},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.14374v3}
}

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