Laplace-fPINNs: Laplace-Based Fractional Physics-Informed Neural Networks for Solving Forward and Inverse Problems of a Time Fractional Equation

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Abstract
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. Physics-informed neural networks, Laplace transform, numerical inverse Laplace transform, time fractional equations. 35R11 COPYRIGHT: © Global Science Press

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