- Journal Home
- Volume 18 - 2025
- Volume 17 - 2024
- Volume 16 - 2023
- Volume 15 - 2022
- Volume 14 - 2021
- Volume 13 - 2020
- Volume 12 - 2019
- Volume 11 - 2018
- Volume 10 - 2017
- Volume 9 - 2016
- Volume 8 - 2015
- Volume 7 - 2014
- Volume 6 - 2013
- Volume 5 - 2012
- Volume 4 - 2011
- Volume 3 - 2010
- Volume 2 - 2009
- Volume 1 - 2008
Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 487-520.
Published online: 2025-05
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0100 }, url = {http://global-sci.org/intro/article_detail/nmtma/24073.html} }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.