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arXiv · 2307.14395

Learning to simulate partially known spatio-temporal dynamics with trainable difference operators

Xiang Huang·Zhuoyuan Li·Hongsheng Liu·Zidong Wang·Hongye Zhou·Bin Dong·Bei Hua
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Abstract

Recently, using neural networks to simulate spatio-temporal dynamics has received a lot of attention. However, most existing methods adopt pure data-driven black-box models, which have limited accuracy and interpretability. By combining trainable difference operators with black-box models, we propose a new hybrid architecture explicitly embedded with partial prior knowledge of the underlying PDEs named PDE-Net++. Furthermore, we introduce two distinct options called the trainable flipping difference layer (TFDL) and the trainable dynamic difference layer (TDDL) for the difference operators. Numerous numerical experiments have demonstrated that PDE-Net++ has superior prediction accuracy and better extrapolation performance than black-box models.

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Xiang Huang, Zhuoyuan Li, Hongsheng Liu, Zidong Wang, Hongye Zhou, Bin Dong, Bei Hua. 2023-07-26. Learning to simulate partially known spatio-temporal dynamics with trainable difference operators. https://arxiv.org/abs/2307.14395

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