TY - JOUR

T1 - Data-driven operator inference for nonintrusive projection-based model reduction

AU - Peherstorfer, Benjamin

AU - Willcox, Karen

N1 - Funding Information:
This work was supported in part by the United States Department of Energy, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program , awards DE-FG02-08ER2585 and DE-SC0009297 , as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center. Some of the numerical examples were computed on the computer cluster of the Munich Centre of Advanced Computing.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - This work presents a nonintrusive projection-based model reduction approach 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 demonstrate operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order.

AB - This work presents a nonintrusive projection-based model reduction approach 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 demonstrate operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order.

KW - Black-box full model

KW - Data-driven model reduction

KW - Inference

KW - Nonintrusive model reduction

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U2 - 10.1016/j.cma.2016.03.025

DO - 10.1016/j.cma.2016.03.025

M3 - Article

AN - SCOPUS:84964334130

VL - 306

SP - 196

EP - 215

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -