Long-time integration of partial differential equations based on a sliding-interval physics-informed neural network.

As a deep learning-based framework, the physics-informed neural network (PINN) has been widely used to solve partial differential equations (PDEs) in various fields. However, due to causality violation and activation function saturation, PINN typically suffers from poor performance in long-time integration tasks. To address these issues, we propose a variant of PINN named sliding-interval PINN (SI-PINN). First, SI-PINN decomposes the temporal domain and employs a sliding-interval strategy to avoid activation function saturation. It also integrates a pretraining scheme to mitigate causality violation in PINN, thereby enabling long-time integration of PDEs. To validate the effectiveness of our SI-PINN, the proposed strategy is evaluated on a set of typical PDEs and compared with existing methods. Numerical results demonstrate that it enables accurate long-time integration across various systems. Moreover, in most cases we examined, it achieves superior accuracy to that of existing methods. The proposed SI-PINN is expected to provide a promising strategy for long-time integration of PDEs.