DSAIS-PINN: Dynamic seeds allocation importance sampling for physics-informed neural networks

Wentao Feng, Ming Hu, Rui Huang, Chenwei Tang, Shudong Huang, Jiancheng Lv

Abstract: Highlights•This paper presents a novel Dynamic Seed Allocation Importance Sampling (DSAIS) method, enabling the PINNs to concentrate on high-loss regions and enhance solution accuracy.•The integration of importance sampling techniques into the training of PINNs substantially improves convergence rates and overall computational efficiency, addressing key limitations of conventional PINNs.•The proposed method’s effectiveness is demonstrated through several benchmark equations, including Schrödinger, Burgers, Korteweg–de Vries equations, and the 2D heat equation.