Cameron Musco 

Associate Professor at University of Massachusetts Amherst 

Traditional machine learning methods seek to learn functions that map vector-valued input data to scalar-valued outputs or labels. Increasingly, however, applications in scientific machine learning (SciML) and other areas require models that map vector-valued data to vector-valued data. Such operator learning methods have been critical to recent breakthroughs in computational science, including on AI-driven methods for weather prediction, PDE solving, and more.

In this talk, I will discuss a research program that seeks to understand the sample complexity of operator learning, which is a critical bottleneck in many applications. We focus in particular on the problem of learning linear operators -- i.e., matrices. Even this restricted setting leads to many interesting theoretical questions. I will highlight recent work that tackles some of these questions by leveraging tools from randomized numerical linear algebra (RandNLA). I will also discuss our efforts to develop a general learning theory for linear operators.

The talk will be accessible to a general computing audience.