PINN neural network method for solving the forward and inverse problem of time-fractional telegraph equation

In this paper, the PINN neural networks method is used to solve the forward and inverse problems of two types of the time-fractional telegraph equation. The forward problem is to calculate the value of u ( x , t ) through specific equations, initial values, and boundary conditions, while the inverse problem is to invert the value of the source term f ( x , t ) and initial value u ( x , 0 ) through the terminal value condition u ( x , T ) = g ( x ) with errors and boundary conditions. Moreover, four improved PINN neural networks: PINN, PINN-LRA, PINN-W and PINN-RAR, are used to identify the source term and invert the value of the original function. Through data comparison, these four methods are very effective in solving inverse problems of the time-fractional telegraph. • PINN neural networks are used to solve the forward and inverse problems time-fractional telegraph equation. • The forward problem is to calculate the value of u(x,t). • The inverse problem is to invert the value of the source term f(x,t) and initial value u(x, 0). • Four improved PINN neural networks are used to identify the source term and invert the value. • These four methods are very effective in solving inverse problems of the time-fractional telegraph.