#### Conference abstracts

Session A6 - Mathematical Foundations of Data Assimilation and Inverse Problems

July 10, 16:00 ~ 16:30

## Data-driven operator inference for non-intrusive projection-based model reduction

### Karen Willcox

### MIT, USA - kwillcox@mit.edu

This talk presents a non-intrusive projection-based model reduction approach for full models based on time-dependent partial differential equations. Projection-based model reduction constructs the operators of a reduced model by projecting the equations of the full model onto a reduced space. Traditionally, this projection is intrusive, which means that the full-model operators are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a given vector; however, in many situations the full model is given as a black box that computes trajectories of the full-model states and outputs for given initial conditions and inputs, but does not provide the full-model operators. Our non-intrusive operator inference approach solves an optimization problem to infer approximations of the reduced operators from the initial conditions, inputs, trajectories of the states, and outputs of the full model, without requiring the full-model operators. The inferred operators are the solution of a least-squares problem and converge, with sufficient state trajectory data, in the Frobenius norm to the reduced operators that would be obtained via an intrusive projection of the full-model operators.

Reference: Peherstorfer, B. and Willcox, K., Data-driven operator inference for nonintrusive projection-based model reduction, Computer Methods in Applied Mechanics and Engineering, Vol. 306, pp. 196-215, 2016.

Joint work with Benjamin Peherstorfer (University of Wisconsin - Madison).