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Preprints, Working Papers, ... Year : 2023

Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network

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 simultaneously learn the encoder-decoder operators and the reduced dynamics. 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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Dates and versions

hal-04237799 , version 1 (11-10-2023)
hal-04237799 , version 2 (10-11-2023)

Identifiers

  • HAL Id : hal-04237799 , version 2

Cite

Raphaël Côte, Emmanuel Franck, Laurent Navoret, Guillaume Steimer, Vincent Vigon. Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network. 2023. ⟨hal-04237799v2⟩
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