TY - JOUR
T1 - On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs
AU - Sheng , Rui
AU - Yang , Jerry Zhijian
AU - Yuan , Cheng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 487
EP - 520
PY - 2025
DA - 2025/05
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0100 
UR - https://global-sci.org/intro/article_detail/nmtma/24073.html
KW - MC-fPINNs, fractional evolution PDEs, inverse source problem.
AB - <p style="text-align: justify;">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.</p>