Statistics and Data Science Seminar: "Depth separation in dimensionality reduction of nonlinear waves"

Abstract: When solutions to parametrized partial differential equations often lie in a low-dimensional linear space, it enables one to numerically compute the solution for all parameters efficiently. However, for solutions that describe wave phenomena, the solutions typically do not yield linearly low-dimensional approximations. In this talk, we will describe how a nonlinear low-dimensional approximations in the form of deep neural networks can represent such solutions. We will also illustrate a form of "depth-separation" for these constructions: this term broadly refers to the existence of approximation tasks that deeper neural networks can achieve but shallower ones cannot.

Hosts: Debashis Mondal and Likai Chen