Improving the efficiency of training physics-informed neural networks using active learning

Abstract

PINN is a PDE solver realized as a neural network by incorporating the PDEs to be satisfied into the network as physical constraints. In this study, focusing on how to select the collocation points, we propose an active learning method to improve the efficiency of PINN learning. The proposed method uses variational inference based on dropout learning to evaluate the uncertainty of the solution estimate by PINN and defines an acquisition function for active learning based on the uncertainty. Then, by probabilistically sampling collocation points using the acquisition function, a reasonable solution can be obtained faster than random sampling. We demonstrate the effectiveness of the method using Burgers’ equation and the convection equation. We also show experimentally that the choice of the collocation points can affect the loss function, the fitting of initial and boundary conditions, and the sensible balance of PDE constraints.