TY - JOUR
T1 - Hamiltonian Reduction Using a Convolutional Auto-Encoder Coupled to a Hamiltonian Neural Network
AU - Côte , Raphaël
AU - Franck , Emmanuel
AU - Navoret , Laurent
AU - Steimer , Guillaume
AU - Vigon , Vincent
JO - Communications in Computational Physics
VL - 2
SP - 315
EP - 352
PY - 2025
DA - 2025/02
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2023-0300
UR - https://global-sci.org/intro/article_detail/cicp/23866.html
KW - Hamiltonian dynamics, model order reduction, convolutional auto-encoder, Hamiltonian neural network, non-linear wave equations, shallow water equation.
AB - <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>