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
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.