TY - JOUR

T1 - Learning Nonlinear Reduced Models from Data with Operator Inference

AU - Kramer, Boris

AU - Peherstorfer, Benjamin

AU - Willcox, Karen E.

N1 - Publisher Copyright:
© 2024 by the author(s).

PY - 2024/1/19

Y1 - 2024/1/19

N2 - This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

AB - This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

KW - Operator Inference

KW - data-driven modeling

KW - nonlinear model reduction

KW - scientific machine learning

KW - structure preservation

UR - http://www.scopus.com/inward/record.url?scp=85182316360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85182316360&partnerID=8YFLogxK

U2 - 10.1146/annurev-fluid-121021-025220

DO - 10.1146/annurev-fluid-121021-025220

M3 - Review article

AN - SCOPUS:85182316360

SN - 0066-4189

VL - 56

SP - 521

EP - 548

JO - Annual Review of Fluid Mechanics

JF - Annual Review of Fluid Mechanics

ER -