@Article{NMTMA-18-487,
author = {Sheng , RuiYang , Jerry Zhijian and Yuan , Cheng},
title = {On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2025},
volume = {18},
number = {2},
pages = {487--520},
abstract = {<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>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0100 },
url = {http://global-sci.org/intro/article_detail/nmtma/24073.html}
}