Symplectic convolutional neural networks
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914307063676928 |
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| author | Yıldız, Süleyman Janik, Konrad Benner, Peter |
| author_facet | Yıldız, Süleyman Janik, Konrad Benner, Peter |
| contents | We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form of the convolution layer and then, using symplectic neural networks, we demonstrate a way to parameterize the layers of the CNN to ensure that the convolution layer remains symplectic. To construct a complete autoencoder, we introduce a symplectic pooling layer. We demonstrate the performance of the proposed neural network on three examples: the wave equation, the nonlinear Schrödinger (NLS) equation, and the sine-Gordon equation. The numerical results indicate that the symplectic CNN outperforms the linear symplectic autoencoder obtained via proper symplectic decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symplectic convolutional neural networks Yıldız, Süleyman Janik, Konrad Benner, Peter Machine Learning We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form of the convolution layer and then, using symplectic neural networks, we demonstrate a way to parameterize the layers of the CNN to ensure that the convolution layer remains symplectic. To construct a complete autoencoder, we introduce a symplectic pooling layer. We demonstrate the performance of the proposed neural network on three examples: the wave equation, the nonlinear Schrödinger (NLS) equation, and the sine-Gordon equation. The numerical results indicate that the symplectic CNN outperforms the linear symplectic autoencoder obtained via proper symplectic decomposition. |
| title | Symplectic convolutional neural networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.19842 |