{"ID":2877629,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19842","arxiv_id":"2508.19842","title":"Symplectic convolutional neural networks","abstract":"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.","short_abstract":"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 demonstr...","url_abs":"https://arxiv.org/abs/2508.19842","url_pdf":"https://arxiv.org/pdf/2508.19842v2","authors":"[\"Süleyman Yıldız\",\"Konrad Janik\",\"Peter Benner\"]","published":"2025-08-27T12:55:24Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Convolutional Neural Network\"]","has_code":false}