mlsanityData to 14 Oct 2026

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

arXiv 2304.00909 ↗First posted 3 Apr 2023math.NA cs.LG cs.NAcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 18 of its 45 references that are in the map. First posted on arXiv 3 Apr 2023.

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18 of 45 references.

References · 18

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6 more
  1. 2020Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domainscited by 79
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  5. 2022Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equationscited by 20
  6. 2022Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problemscited by 1

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Citing papers per year: 2023: 1.

1 paper.

  1. 2023HNS: An Efficient Hermite Neural Solver for Solving Time-Fractional Partial Differential Equationscited by 0