TY - JOUR

T1 - Automated and efficient local adaptive regression for principal component-based reduced-order modeling of turbulent reacting flows

AU - D'Alessio, Giuseppe

AU - Sundaresan, Sankaran

AU - Mueller, Michael E.

N1 - Funding Information:
The authors gratefully acknowledge funding from the University Coalition for Fossil Energy Research through the U.S. Department of Energy's National Energy Technology Laboratory (DE-FE0026825) and from the Schmidt DataX Fund at Princeton University made possible through a major gift from the Schmidt Futures Foundation. The simulations presented in this article were performed on computational resources supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology's High Performance Computing Center and Visualization Laboratory at Princeton University.
Funding Information:
The authors gratefully acknowledge funding from the University Coalition for Fossil Energy Research through the U.S. Department of Energy’s National Energy Technology Laboratory (DE-FE0026825) and from the Schmidt DataX Fund at Princeton University made possible through a major gift from the Schmidt Futures Foundation. The simulations presented in this article were performed on computational resources supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology’s High Performance Computing Center and Visualization Laboratory at Princeton University.
Publisher Copyright:
© 2022 The Combustion Institute

PY - 2023/1

Y1 - 2023/1

N2 - Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. In this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.

AB - Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. In this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.

KW - Bayesian optimization

KW - Local regression

KW - Machine learning

KW - Principal Component Analysis

KW - Turbulent flames

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U2 - 10.1016/j.proci.2022.07.235

DO - 10.1016/j.proci.2022.07.235

M3 - Article

AN - SCOPUS:85138738658

SN - 1540-7489

VL - 39

SP - 5249

EP - 5258

JO - Proceedings of the Combustion Institute

JF - Proceedings of the Combustion Institute

IS - 4

ER -