Speaker: Donsub Rim (NYU)

Title: Nonlinear model reduction of wave propagation: depth separation and the Radon transform

Model reduction aims to construct a low-dimensional reduced model to drastically cut down computation times for many-query problems involving large-scale numerical solvers. However, well-established methods are inefficient for the simplest wave propagation problems. This talk will focus on two recent proposals on how to overcome this limitation. The first is a nonlinear reduced model taking on the form of deep neural networks that exhibits a type of depth-separation in dimensionality reduction. The second is the use of the Radon transform to exploit a similar structure in multi-dimensional problems. A particularly suitable discretization of the Radon transform, called the approximate discrete Radon transform (ADRT), and its properties will also be discussed.

This talk is based on joint works with Joan Bruna, Weilin Li, Kyle T. Mandli, Benjamin Peherstorfer, Kui Ren, and Luca Venturi.