Title: Algorithm Design and Approximation Using DNNs

Speaker: Harbir Antil, George Mason University

Abstract: This talk begins by addressing the question whether DNNs can be used to generate algorithms and not just function approximations. This is explored with the help of an example where a DNN architecture is shown to be the exact equivalent of explicit Runge-Kutta time integrator. Remarkably, the weights and biases are given, i.e., no training is needed. The second part of the talk focuses on designing efficient DNN architectures to approximate solutions to parameterized PDEs and inverse problems. Efficiency arise by introducing nonlocality and by reducing the DNN parameter search space. With the help of various examples in fluid dynamics, wave equations, and complex flows, the efficiency of these networks is illustrated without sacrificing the accuracy.