Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion
Year: 2023
Type: preprint
Abstract: The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional derivatives, solving fractional diffusion equations using PINNs requires addressing additional challenges. To address this issue, this paper proposes an extension to PINNs called Laplace-based fractional physics-informed neural networks (Laplace-fPINNs), which can effectively solve the forward and inverse problems of fractional diffusion equations. This approach avoids introducing a mass of auxiliary points and simplifies the loss function. We validate the effectiveness of the Laplace-fPINNs approach using several examples. Our numerical results demonstrate that the Laplace-fPINNs method can effectively solve both the forward and inverse problems of high-dimensional fractional diffusion equations.
Source: arXiv (Cornell University)
Authors: Yan, Xiong-Bin, Xu, Zhi-Qin John, Ma, Zheng
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4362631760