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

TL;DR

This paper introduces PDE-Net++, a hybrid neural network architecture that integrates trainable difference operators with black-box models to improve the simulation of spatio-temporal dynamics, leveraging partial prior knowledge of PDEs.

Contribution

The paper presents PDE-Net++, a novel hybrid model combining trainable difference operators with neural networks, enhancing accuracy and interpretability in simulating PDE-based dynamics.

Findings

PDE-Net++ outperforms pure black-box models in prediction accuracy.

The model demonstrates superior extrapolation capabilities.

Two new difference operator layers, TFDL and TDDL, are introduced.

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.