The influence of the optimization algorithm in the solution of the fractional Laplacian equation by neural networks.

In this paper, the influence of the optimization algorithms Adam, RMSprop, L-BFGS and SGD with momentum on the solution of Fractional Laplacian Equation (FLE) by physics-informed neural networks is analysed when considering two different analytical solutions, one smooth and one non-smooth. The influence of the optimization method, the smoothness of the analytical solution and the network configuration on the accuracy of the predicted solution is discussed in detail. [ABSTRACT FROM AUTHOR]