Andrew Stuart - Supervised Learning For Operators

Prof. Andrew Stuart from Caltech speaking in the UW Data-driven methods in science and engineering seminar on May 6, 2022.

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Abstract: Consider map F: U \to V. Given data pairs {u_j,F(u_j)} the goal of supervised learning is to approximate F. Neural networks have shown considerable success in addressing this problem in settings where X is a finite dimensional Euclidean space and where Y is either a finite dimensional Euclidean space (regression) or a set of finite cardinality (classification). Motivated by the need for surrogate modeling (in, for example, Bayesian inversion) and by scientific discovery (in, for example, constitutive modeling) we focus on the design and analysis of algorithms which address supervised learning for settings where U and V comprise spaces of functions; thus F is an operator. The talk describes emerging methodology in this area, emerging theory which underpins the methodology and numerical experiments which elucidate the efficiency of different approaches. Various applications from continuum mechanics are described, including an inverse problem arising in incompressible fluid flow and constitutive modeling in viscoelasticity.