Quasi-Optimal Sampling to Learn Basis Updates for Online Adaptive Model Reduction with Adaptive Empirical Interpolation

Alice Cortinovis, Daniel Kressner, Stefano Massei, Benjamin Peherstorfer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Traditional model reduction derives reduced models from large-scale systems in a one-time computationally expensive offline (training) phase and then evaluates reduced models in an online phase to rapidly predict system outputs; however, this offline/online splitting means that reduced models can be expected to faithfully predict outputs only for system behavior that has been incorporated into the reduced models during the offline phase. This work considers model reduction with the online adaptive empirical interpolation method (AADEIM) that adapts reduced models in the online phase to system behavior that was not anticipated in the offline phase by deriving updates from a few samples of the states of the large-scale systems. The contribution of this work is an analysis of the AADEIM sampling strategy for deciding which parts of the large-scale states to sample to learn reduced-model updates. The analysis shows that the AADEIM sampling strategy is optimal up to a factor 2. Numerical results demonstrate the theoretical results by comparing the quasi-optimal AADEIM sampling strategy to other sampling strategies on various examples.

Original languageEnglish (US)
Title of host publication2020 American Control Conference, ACC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2472-2477
Number of pages6
ISBN (Electronic)9781538682661
DOIs
StatePublished - Jul 2020
Event2020 American Control Conference, ACC 2020 - Denver, United States
Duration: Jul 1 2020Jul 3 2020

Publication series

NameProceedings of the American Control Conference
Volume2020-July
ISSN (Print)0743-1619

Conference

Conference2020 American Control Conference, ACC 2020
CountryUnited States
CityDenver
Period7/1/207/3/20

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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