Improving the Efficiency of Training Physics-Informed Neural Networks Using Active Learning

Yuri Aikawa, Naonori Ueda, Toshiyuki Tanaka

Abstract: PINN, or physics-informed neural network, is a partial differential equation (PDE) solver realized as a neural network by incorporating the target PDE into the network as physical constraints. In this study, our focus lies in optimizing collocation point selection. We propose an active learning method to enhance the efficiency of PINN learning. The proposed method leverages variational inference based on dropout learning to assess the uncertainty inherent in the solution estimates provided by the PINN. Subsequently, it formulates an acquisition function for active learning grounded in this uncertainty assessment. By employing this acquisition function to probabilistically select collocation points, we can achieve a more expedited convergence to a reasonable solution, as opposed to relying on random sampling. The efficacy of our approach is empirically demonstrated using both 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.