Karen Willcox
Director, Oden Institute for Computational Engineering and Sciences

Full talk title: Learning physics-based models from data: Perspectives from model reduction

ABSTRACT: Operator Inference is a method for learning predictive reduced-order models from data. The method targets the derivation of a reduced-order model of an expensive high-fidelity simulator that solves known governing equations. Rather than learn a generic approximation with weak enforcement of the physics, we learn low-dimensional operators whose structure is defined by the physical problem being modeled. These reduced operators are determined by solving a linear least squares problem, making Operator Inference scalable to high-dimensional problems. The method is entirely non-intrusive, meaning that it requires simulation snapshot data but does not require access to or modification of the high-fidelity source code. For problems where the complexity of the physics does not admit a global low-rank structure, we construct a nonlinear approximation space. This is achieved via clustering to obtain localized Operator Inference models, or by approximation in a quadratic manifold. The methodology is demonstrated on challenging large-scale problems arising in rocket combustion and materials phase-field applications.