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Pseudo-Hamiltonian neural networks for learning partial differential equations

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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Category

Academic article

Language

English

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics

Year

2024

Published in

Journal of Computational Physics

ISSN

0021-9991

Volume

500

View this publication at Norwegian Research Information Repository