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The use of Physics-informed neural networks (PINNs) has shown promise insolving forward and inverse problems of fractional diffusion equations.However, due to the fact that automatic differentiation is not applicable forfractional derivatives, solving fractional diffusion equations using PINNsrequires addressing additional challenges. To address this issue, this paperproposes an extension to PINNs called Laplace-based fractional physics-informedneural networks (Laplace-fPINNs), which can effectively solve the forward andinverse problems of fractional diffusion equations. This approach avoidsintroducing a mass of auxiliary points and simplifies the loss function. Wevalidate the effectiveness of the Laplace-fPINNs approach using severalexamples. Our numerical results demonstrate that the Laplace-fPINNs method caneffectively solve both the forward and inverse problems of high-dimensionalfractional diffusion equations.

Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion