A novel fractional physics-informed neural networks method for solving the time-fractional Huxley equation

The neural network methods in solving differential equations have significant research importance and promising application prospects. Aimed at the time-fractional Huxley (TFH) equation, we propose a novel fractional physics-informed neural networks (fPINNs) method. By integrating the physical information of the TFH equation into neural networks, the fPINNs are trained as a precise approximation model for solving the TFH equation. The fPINNs method involves calculating the Caputo fractional derivative using the L1 formula and estimating the integer-order derivative through the chain rule. The Adam algorithm is employed to optimize two kinds of loss functions constructed by hard and soft constraints, respectively. Through an analysis of the impact of fPINNs parameters on training results, we identify the optimal parameter configuration for solving both one-dimensional and two-dimensional (2D) TFH equations. Numerical examples validate the efficiency and robustness of the fPINNs method in solving TFH equations. Furthermore, numerical simulation of the 2D TFH problem demonstrates the method’s practical applicability to engineering problem.