Data-Driven Reduced Model Construction with Time-Domain Loewner Models
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Author(s)
Gugercin, Serkan
Peherstorfer, Benjamin
Willcox, Karen E
Date Issued
September 2017
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Peherstorfer, Benjamin, et al. “Data-Driven Reduced Model Construction with Time-Domain Loewner Models.” SIAM Journal on Scientific Computing, vol. 39, no. 5, Jan. 2017, pp. A2152–78. © 2017 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
This work presents a data-driven nonintrusive model reduction approach for large-scale time-dependent systems with linear state dependence. Traditionally, model reduction is performed in an intrusive projection-based framework, where the operators of the full model are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a vector. Our nonintrusive approach constructs reduced models directly from trajectories of the inputs and outputs of the full model, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model; our method then infers frequency-response data from these simulated time-domain trajectories and uses the data-driven Loewner framework to derive a reduced model. Only a single time-domain simulation is required to derive a reduced model with the new data-driven nonintrusive approach. We demonstrate our model reduction method on several benchmark examples and a finite element model of a cantilever beam; our approach recovers the classical Loewner reduced models and, for these problems, yields high-quality reduced models despite treating the full model as a black box. Key words: data-driven model reduction, nonintrusive model reduction, projection-based
reduced models, Loewner framework, black-box models, dynamical systems, partial differential equations
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/16M1094750
