CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networks

arXiv:2208.08626v3 Announce Type: replace-cross
Abstract: We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal approximators capable of estimating the solution of any physical law described by a system of PDEs, which serves as a regularization during neural network training, restricting the space of admissible solutions and enhancing function approximation accuracy. We demonstrate that when the …

abstract arxiv cs.ai cs.lg cs.na data data-driven detection differential dynamics math.ds math.na networks neural networks parameters physics physics-informed random solution stat.ml type universal