Symplectic convolutional neural networks

• URL: http://arxiv.org/abs/2508.19842v1
• Date: Wed, 27 Aug 2025 12:55:24 GMT
• Title: Symplectic convolutional neural networks
• Authors: Süleyman Yıldız, Konrad Janik, Peter Benner,
• Abstract summary: We propose a new symplectic convolutional neural network (CNN) architecture.<n>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.<n>To construct a complete autoencoder, we introduce a symplectic pooling layer.
• Score: 0.9379969114114787
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Schr\"odinger (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.

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