Fractional physics-informed neural networks for time-fractional phase field models

In this paper, a new fractional physics-informed neural networks (fPINNs) is proposed, which combines fPINNs with spectral collocation method to solve the time-fractional phase field models. Compared fPINNs, it has large representation capacity due property of method, reduces number approximate points discrete operators, improves training efficiency and higher error accuracy. Unlike traditional numerical directly optimizes coefficient, saves time matrix calculation, easy deal high-dimensional model, also First, based on used obtain solutions models under consideration. The discretize space direction, backward difference formula derivative. accuracy in different cases discussed, observed that point-wise $$10^{-5}$$ $$10^{-7}$$ . Next, employed several inverse problems identify order derivative, mobility constant, other coefficients. results experiments are presented prove effectiveness solving their problems.