Year: 2025
Type: article
Abstract: In this paper, we solve the inverse source problem of fractional evolution PDEs by MC-fPINNs. We construct the loss function in terms of the governing equation residual, boundary residual, initial residual and measurement data with noise. Meanwhile, we present a rigorous error analysis of this method. In the experimental section, we present the reconstruction outcomes of the source term for three evolutionary fractional partial differential equations (fPDEs): the evolutionary fractional Laplacian equation, the time-space fractional diffusion equation, and the fractional advection-diffusion equation. These experiments illustrate robust performance of MC-fPINNs in both low-dimensional and high-dimensional scenarios. Our results confirm the effectiveness of MC-fPINNs in solving such inverse source problem, and also provide a theoretical foundation to choose neural networks parameters in this algorithm.
Authors: Rui Sheng, Jerry Zhijian Yang, Cheng Yuan
Institutions: Wuhan University, Central China Normal University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4408895489