TY - JOUR
T1 - Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
AU - Benner, Peter
AU - Goyal, Pawan
AU - Kramer, Boris
AU - Peherstorfer, Benjamin
AU - Willcox, Karen
N1 - Funding Information:
This work was supported in part by the US Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics award FA9550-17-1-0195, the Air Force Office of Scientific Research, United States MURI on managing multiple information sources of multi-physics systems awards FA9550-15-1-0038 and FA9550-18-1-0023, and the AEOLUS, United States center under US Department of Energy Applied Mathematics MMICC award DE-SC0019303. The fourth author was partially supported by the US Department of Energy, Office of Advanced Scientific Computing Research, United States, Applied Mathematics Program, United States, DOE, United States Award DESC0019334 and the National Science Foundation, United States under Grant No. 1901091.
Funding Information:
This work was supported in part by the US Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics award FA9550-17-1-0195 , the Air Force Office of Scientific Research, United States MURI on managing multiple information sources of multi-physics systems awards FA9550-15-1-0038 and FA9550-18-1-0023 , and the AEOLUS, United States center under US Department of Energy Applied Mathematics MMICC award DE-SC0019303 . The fourth author was partially supported by the US Department of Energy , Office of Advanced Scientific Computing Research, United States , Applied Mathematics Program, United States , DOE, United States Award DESC0019334 and the National Science Foundation, United States under Grant No. 1901091 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.
AB - This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated on the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion–reaction Chafee–Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.
KW - Data-driven modeling
KW - Model reduction
KW - Nonlinear dynamical systems
KW - Operator inference
KW - Scientific machine learning
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U2 - 10.1016/j.cma.2020.113433
DO - 10.1016/j.cma.2020.113433
M3 - Article
AN - SCOPUS:85092089430
SN - 0374-2830
VL - 372
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113433
ER -