Year: 2025
Author: Raphaël Côte, Emmanuel Franck, Laurent Navoret, Guillaume Steimer, Vincent Vigon
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 315–352
Abstract
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain long-term stability properties can be preserved. In this paper, we propose a non-linear reduction method for models coming from the spatial discretization of partial differential equations: it is based on convolutional auto-encoders and Hamiltonian neural networks. Their training is coupled in order to learn the encoder-decoder operators and the reduced dynamics simultaneously. Several test cases on non-linear wave dynamics show that the method has better reduction properties than standard linear Hamiltonian reduction methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0300
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 315–352
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Hamiltonian dynamics model order reduction convolutional auto-encoder Hamiltonian neural network non-linear wave equations shallow water equation.