Learning to simulate partially known spatio-temporal dynamics with trainable difference operators
This work addresses the need for more accurate and interpretable simulation methods in fields like physics and engineering, though it is incremental as it builds on prior hybrid approaches.
The authors tackled the problem of simulating spatio-temporal dynamics with limited accuracy and interpretability in neural network models by proposing PDE-Net++, a hybrid architecture that combines trainable difference operators with black-box models, resulting in superior prediction accuracy and better extrapolation performance compared to black-box models.
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.