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arXiv · 2508.19842

Symplectic convolutional neural networks

Süleyman Yıldız·Konrad Janik·Peter Benner
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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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Süleyman Yıldız, Konrad Janik, Peter Benner. 2025-08-27. Symplectic convolutional neural networks. https://arxiv.org/abs/2508.19842

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