GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains

arXiv:2405.00217v1 Announce Type: new
Abstract: Physics-Informed Neural Networks (PINNs) have been widely used for solving partial differential equations (PDEs) of different types, including fractional PDEs (fPDES) [29]. Herein, we propose a new general (quasi) Monte Carlo PINN for solving fPDEs on irregular domains. Specifically, instead of approximating fractional derivatives by Monte Carlo approximations of integrals as was done previously in [31], we use a more general Monte Carlo approximation method to solve different fPDEs, which is valid for fractional differentiation …

abstract arxiv cs.lg differential domains general networks neural networks physics physics-informed pinn type types