Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913500894330880 |
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| author | Côte, Raphaël Franck, Emmanuel Navoret, Laurent Steimer, Guillaume Vigon, Vincent |
| author_facet | Côte, Raphaël Franck, Emmanuel Navoret, Laurent Steimer, Guillaume Vigon, Vincent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network Côte, Raphaël Franck, Emmanuel Navoret, Laurent Steimer, Guillaume Vigon, Vincent Numerical Analysis 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. |
| title | Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2311.06104 |