Efficient 𝐻₂-Based Parametric Model Reduction via Greedy Search

Dynamical systems are mathematical models of physical phenomena widely used throughout the world today. When a dynamical system is too large to effectively use, we turn to model reduction to obtain a smaller dynamical system that preserves the behavior of the original. In many cases these models depend on one or more parameters other than time, which leads to the field of parametric model reduction.

Constructing a parametric reduced-order model (ROM) is not an easy task, and for very large parametric systems it can be difficult to know how well a ROM models the original system, since this usually involves many computations with the full-order system, which is precisely what we want to avoid. Building off of efficient 𝐻-infinity approximations, we develop a greedy algorithm for efficiently modeling large-scale parametric dynamical systems in an 𝐻₂-sense.

We demonstrate the effectiveness of this greedy search on a fluid problem, a mechanics problem, and a thermal problem. We also investigate Bayesian optimization for solving the optimization subproblem, and end with extending this algorithm to work with MIMO systems.