Fs‐Pinns: Fractional Spectrally Adapted Physics‐Informed Neural Networks for Fractional Partial Differential Equations

Source abstract

ABSTRACT In this paper, we present a new and efficient fractional spectrally adapted physics‐informed neural network (fs‐PINN) method for solving fractional partial differential equations (PDEs). The fs‐PINN approach overcomes the computational difficulties encountered by traditional methods and standard physics‐informed neural networks (PINNs) in solving fractional PDEs on unbounded domains. We transform the nonlocal fractional PDEs into local equations in a higher dimensional space through extension, addressing numerical difficulties associated with nonlocal fractional operators. This local form is then combined with spectrally adapted PINNs (s‐PINNs) to develop the fs‐PINN approach, which effectively handles unbounded domains. Our numerical experiments show that the fs‐PINN algorithm achieves comparable performance to the fPINN algorithm in bounded domains. In contrast to fPINN, the advantage of fs‐PINN is its capability for the case of unbounded domains.