Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion
This is an incremental improvement for researchers in computational physics and machine learning, addressing specific bottlenecks in fractional derivative modeling.
The paper tackled the challenge of solving fractional diffusion equations with physics-informed neural networks (PINNs) by proposing Laplace-fPINNs, which avoids automatic differentiation issues and simplifies the loss function, demonstrating effectiveness in forward and inverse problems for high-dimensional equations.
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.