In this talk, we propose a new symplectic convolutional neural network (CNN) architecture [1] by leveraging symplectic neural networks [2], proper symplectic decomposition (PSD) [3], and tensor techniques. Specifically, we first introduce a mathematically equivalent formulation of the convolutional layer and then, using symplectic neural networks, demonstrate how to parameterize the layers of a CNN such that the convolutional layers remain symplectic. Furthermore, we use this novel architecture to construct a symplectic convolutional autoencoder. Currently, one must either enforce symplecticity weakly [4] or avoid convolutional layers altogether [5]. By employing our new symplectic convolutional layers, we can enforce symplecticity strongly, i.e., by design, while benefiting from the fast forward pass and low-dimensional parameter space offered by convolutional layers. In addition, we introduce symplectic pooling layers to ensure the availability of symplectic counterparts to all layer types commonly used in convolutional autoencoders [6]. We demonstrate the performance of the proposed neural network on three examples: the wave equation, the nonlinear Schrödinger equation, and the sine-Gordon equation. The numerical results indicate that the symplectic autoencoder outperforms the linear symplectic autoencoder obtained via PSD. References [1] S. Yildiz, K. Janik, P. Benner, Symplectic Concolutional Neural Networks, arXiv:2508.19842, 2025. [2] P. Jin, Z. Zhang, A. Zhu, Y. Tang, G. E. Karniadakis, SympNets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems, Neural Networks, Vol. 132, pp. 166–179, 2020. [3] L. Peng, K. Mohseni, Symplectic model reduction of Hamiltonian systems, SIAM Journal on Scientific Computing, Vol. 38, no. 1, pp. A1–A27, 2016. [4] P. Buchfink, S. Glas, B. Haasdonk, Symplectic model reduction of Hamiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder, SIAM Journal on Scientific Computing, Vol. 45, No. 2, pp. A289–A311, 2023. [5] B. Brantner, M. Kraus, Symplectic autoencoders for model reduction of Hamiltonian systems, arXiv:2312.10004, 2023. [6] A. Krizhevsky, I. Sutskever, G. E. Hinton, Imagenet classification with deep convolutional neural networks, Communications of the ACM, Vol. 60, No. 6, pp. 84–90, 2017.