ABSTRACT:

Operator learning, the data-driven approximation of nonlinear maps between function spaces, and equation learning, the problem of discovering PDEs that govern physical systems, are two focus areas of scientific machine learning and applications of AI in science. In this talk I will discuss mathematically simple, efficient, and competitive methods for both of these tasks using the framework of reproducing Kernel Hilbert spaces. I will also discuss a unifying view point that unites operator and equation learning. Various theoretical results and numerical benchmarks will also be discussed.