The use of Physics-informed neural networks (PINNs) has shown promise in
solving forward and inverse problems of fractional diffusion equations.
However, due to the fact that automatic differentiation is not applicable for
fractional derivatives, solving fractional diffusion equations using PINNs
requires addressing additional challenges. To address this issue, this paper
proposes an extension to PINNs called Laplace-based fractional physics-informed
neural networks (Laplace-fPINNs), which can effectively solve the forward and
inverse problems of fractional diffusion equations. This approach avoids
introducing a mass of auxiliary points and simplifies the loss function. We
validate the effectiveness of the Laplace-fPINNs approach using several
examples. Our numerical results demonstrate that the Laplace-fPINNs method can
effectively solve both the forward and inverse problems of high-dimensional
fractional diffusion equations.

本研究提出了一种称为 Laplace-based fractional physics-informed neural networks (Laplace-fPINNs) 的新方法，通过避免引入大量辅助点和简化损失函数有效解决高维分数扩散方程的正演和反演问题。数值结果证明，Laplace-fPINNs 方法能够有效地解决高维分数扩散方程的正演和反演问题。