TY - JOUR
T1 - Laplace-fPINNs: Laplace-Based Fractional Physics-Informed Neural Networks for Solving Forward and Inverse Problems of a Time Fractional Equation
AU - Yan , Xiong-Bin
AU - Xu , Zhi-Qin John
AU - Ma , Zheng
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 657
EP - 674
PY - 2024
DA - 2024/09
SN - 14
DO - http://doi.org/10.4208/eajam.2023-197.171223
UR - https://global-sci.org/intro/article_detail/eajam/23434.html
KW - Physics-informed neural networks, Laplace transform, numerical inverse Laplace transform, time fractional equations.
AB - <p style="text-align: justify;">Physics-informed neural networks (PINNs) are an efficient tool for solving
forward and inverse problems for fractional diffusion equations. However, since the
automatic differentiation is not applicable to fractional derivatives, solving fractional
diffusion equations by PINNs meets a number of challenges. To deal with the arising
problems, we propose an extension of PINNs called the Laplace-based fractional physics-informed neural networks (Laplace-fPINNs). It can effectively solve forward and inverse
problems for fractional diffusion equations. Note that this approach avoids introducing
a mass of auxiliary points and simplifies the loss function. We validate the effectiveness
of using the Laplace-fPINNs by several examples. The numerical results demonstrate
that the Laplace-fPINNs method can effectively solve the forward and inverse problems
for fractional diffusion equations.</p>