Influence of Activation Functions on the Convergence of Physics-Informed Neural Networks for 1D Wave Equation

In this paper, we consider a model wave equation. We perform a sequence of numerical experiments with Physics Informed Neural Network, considering different activation functions, and different ways of enforcing the initial and boundary conditions. We show the convergence of the method and the resulting numerical accuracy for different setups. We show that, indeed, the PINN methodology can solve the problem efficiently and accurately the wave-equations without actually solving a system of linear equations as it happens in traditional numerical methods like, e.g., finite element or finite difference method. In particular, we compare the influence of selected activation functions on the convergence of the PINN method. Our PINN code is available on github: https://github.com/pmaczuga/pinn-comparison/tree/iccs .