Dynamical model reduction method for solving parameter-dependent dynamical systems

TL;DR

This paper introduces a projection-based model reduction technique for parameter-dependent dynamical systems, utilizing time-dependent reduced spaces and an adaptive greedy algorithm to efficiently approximate solutions with controlled error.

Contribution

It presents a novel dynamical model reduction method that constructs time-dependent reduced spaces and employs an a posteriori error estimate for adaptive parameter selection.

Findings

Effective reduction of computational complexity for parameter-dependent systems

Adaptive greedy algorithm improves approximation accuracy

Provides a uniform error control over parameter space

Abstract

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution of the full-order model at some selected parameters values. The approximation obtained by Galerkin projection is the solution of a reduced dynamical system with a modified flux which takes into account the time dependency of the reduced spaces. An a posteriori error estimate is derived and a greedy algorithm using this error estimate is proposed for the adaptive selection of parameters values. The resulting method can be interpreted as a dynamical low-rank approximation method with a subspace point of view and a uniform control of the error over the parameter set.