Operator Learning: Algorithms, Analysis and Applications

Approximating operators that map between function spaces can be useful for accelerating systems level tasks in scientific computing, and for discovering computational models from data. In its most basic form, learning an operator may be cast as a form of supervised learning in which the input-output pairs are functions. The talk from Cal Tech's Andrew Stuart provides an overview a variety of specific approximation architectures that have been developed in the last five years; emerging theoretical results explaining the approximation capabilities of the architectures will be explained; and applications to constitutive modeling (plasticity) and inverse problems (fluid mechanics) will be given.