Neural Network for Solving Nonlinear Parabolic Differential Equations

We develop a cell-average-based neural network (CANN) method to compute nonlinear differential equations. Using feedforward networks, we can train average solutions from t0 + Δt with initial values. In order to find the optimal parameters for the network, in combination with supervised training, we use a BP algorithm. By the trained network, we may compute the approximate solutions at the time t n+1 with the ones at time tn . Numerical results show CANN method permits a very large time step size for solution evolution.