Fixed-Budget Online Adaptive Learning for Physics-Informed Neural Networks. Towards Parameterized Problem Inference

Thi Nguyen Khoa Nguyen, Thibault Dairay, Raphaël Meunier, Christophe Millet, Mathilde Mougeot

Abstract: Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. The partial differential equations (PDEs) residuals are minimized on a set of collocation points which distribution appears to have a huge impact on the performance of PINNs and the assessment of the sampling methods for these points is still an active topic. In this paper, we propose a Fixed-Budget Online Adaptive Learning (FBOAL) method, which decomposes the domain into sub-domains, for training collocation points based on local maxima and local minima of the PDEs residuals. The numerical results obtained with FBOAL demonstrate important gains in terms of the accuracy and computational cost of PINNs with FBOAL for non-parameterized and parameterized problems. We also apply FBOAL in a complex industrial application involving coupling between mechanical and thermal fields.