@Article{CiCP-37-315,
author = {Côte , RaphaëlFranck , EmmanuelNavoret , LaurentSteimer , Guillaume and Vigon , Vincent},
title = {Hamiltonian Reduction Using a Convolutional Auto-Encoder Coupled to a Hamiltonian Neural Network},
journal = {Communications in Computational Physics},
year = {2025},
volume = {37},
number = {2},
pages = {315--352},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0300},
url = {http://global-sci.org/intro/article_detail/cicp/23866.html}
}