A deep artificial neural network for solving advection equation in half super-ellipse geometry

Abstract

In order to solve the advection equation on a half super elliptical geometry with challenging beginning and boundary conditions, this thesis applies deep artificial neural networks. For arbitrary deep artificial neural networks, we provide analytical formulas of the gradients of the cost function with respect to the network parameters as well as the gradient of the network itself with regard to the input. The approach is based on a solution ansatz that calls for gradient descent and feedforward neural networkS