Applied Mathematics and Statistics presents the Duncan Lecture Series w/ Director Karen Willcox

Abstract: Reduced-order models play a critical role in achieving design, control and uncertainty quantification for complex systems. They are also a key enabling technology for predictive digital twins. 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 of a dynamical system 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. Our recent work has developed an Operator Inference approach that learns a reduced-order model on a quadratic manifold, overcoming some of the limitations of linear subspace approximations. Our reduced-order modeling results are demonstrated for large-scale engineering problems in rocket combustion, additive manufacturing, and materials modeling.