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Title: Data-driven operator inference for nonintrusive projection-based model reduction

Abstract

We presenta a nonintrusive projection-based model reduction method 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 nonintrusive operator inference approach infers 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. Our operator inference is applicable to full models that are linear in the state or have a low-order polynomial nonlinear term. 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. Our numericalmore » results reflect operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order.« less

Authors:
 [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1548303
Alternate Identifier(s):
OSTI ID: 1365588
Grant/Contract Number:  
SC0009297; FG02-08ER2585
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 306; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
Nonintrusive model reduction; Data-driven model reduction; Black-box full model; Inference

Citation Formats

Peherstorfer, Benjamin, and Willcox, Karen. Data-driven operator inference for nonintrusive projection-based model reduction. United States: N. p., 2016. Web. doi:10.1016/j.cma.2016.03.025.
Peherstorfer, Benjamin, & Willcox, Karen. Data-driven operator inference for nonintrusive projection-based model reduction. United States. doi:10.1016/j.cma.2016.03.025.
Peherstorfer, Benjamin, and Willcox, Karen. Wed . "Data-driven operator inference for nonintrusive projection-based model reduction". United States. doi:10.1016/j.cma.2016.03.025. https://www.osti.gov/servlets/purl/1548303.
@article{osti_1548303,
title = {Data-driven operator inference for nonintrusive projection-based model reduction},
author = {Peherstorfer, Benjamin and Willcox, Karen},
abstractNote = {We presenta a nonintrusive projection-based model reduction method 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 nonintrusive operator inference approach infers 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. Our operator inference is applicable to full models that are linear in the state or have a low-order polynomial nonlinear term. 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. Our numerical results reflect operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order.},
doi = {10.1016/j.cma.2016.03.025},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 306,
place = {United States},
year = {2016},
month = {4}
}

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