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。

基于Laplace的分数阶物理信息神经网络Laplace-fPINNs用于解决亚扩散的正向和反向问题