DP-PINN: A Dual-Phase Training Scheme for Improving the Performance of Physics-Informed Neural Networks

Da Yan, Ligang He

Abstract: Physics-Informed Neural Networks (PINNs) are a promising application of deep neural networks for the numerical solution of nonlinear partial differential equations (PDEs). However, it has been observed that standard PINNs may not be able to accurately fit all types of PDEs, leading to poor predictions for specific regions in the domain. A common solution is to partition the domain by time and train each time interval separately. However, this approach leads to the prediction errors being accumulated over time, which is especially the case when solving “stiff” PDEs. To address these issues, we propose a new PINN training scheme, called DP-PINN (Dual-Phase PINN). DP-PINN divides the training into two phases based on a carefully chosen time point \(t_s\). The phase-1 training aims to generate the accurate solution at \(t_s\), which will serve as the additional intermediate condition for the phase-2 training. New sampling strategies are also proposed to enhance the training process. These design considerations improve the prediction accuracy significantly. We have conducted the experiments to evaluate DP-PINN with both “stiff” and non-stiff PDEs. The results show that the solutions predicted by DP-PINN exhibit significantly higher accuracy compared to those obtained by the state-of-the-art PINNs in literature.