An artificial neural network framework for reduced order modeling of transient flows

•An artificial neural network model is proposed for non-intrusive model order reduction of nonlinear systems.•It presents an equation-free approach for predictive reduced order modeling when the control parameter values vary.•The robustness of the model has been tested by considering the viscous Bur...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 77; no. C; pp. 271 - 287
Main Authors: San, Omer, Maulik, Romit, Ahmed, Mansoor
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2019
Elsevier Science Ltd
Elsevier
Subjects:
Artificial intelligence
Artificial neural networks
Burgers equation
Computer simulation
Convective flows
Direct numerical simulation
Evolution
Fluid dynamics
Forecasting
Galerkin method
Learning theory
Machine learning
Mathematical models
Model reduction
Neural networks
Non-intrusive model order reduction
Nonlinear dynamics
Nonlinear equations
Nonlinear systems
Prediction models
Projection model
Proper Orthogonal Decomposition
Reduced order modeling
Reduced order models
Robustness (mathematics)
State variable
Wave propagation
Proper orthogonal decomposition
Reduced order modeling
Convective flows
Non-intrusive model order reduction
Artificial neural networks
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:•An artificial neural network model is proposed for non-intrusive model order reduction of nonlinear systems.•It presents an equation-free approach for predictive reduced order modeling when the control parameter values vary.•The robustness of the model has been tested by considering the viscous Burgers equation.•It is shown that the proposed model could be a viable tool for convective flows. This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our approach utilizes a training process from full-order scale direct numerical simulation data projected on proper orthogonal decomposition (POD) modes to achieve an artificial neural network (ANN) model with reduced memory requirements. This data-driven ANN framework allows for a nonlinear time evolution of the modal coefficients without performing a Galerkin projection. Our POD-ANN framework can thus be considered an equation-free approach for latent space dynamics evolution of nonlinear transient systems and can be applied to a wide range of physical and engineering applications. Within this framework we introduce two architectures, namely sequential network (SN) and residual network (RN), to train the trajectory of modal coefficients. We perform a systematic analysis of the performance of the proposed reduced order modeling approaches on prediction of a nonlinear wave-propagation problem governed by the viscous Burgers equation, a simplified prototype setting for transient flows. We find that the POD-ANN-RN yields stable and accurate results for test problems assessed both within inside and outside of the database range and performs significantly better than the standard intrusive Galerkin projection model. Our results show that the proposed framework provides a non-intrusive alternative to the evolution of transient physics in a POD basis spanned space, and can be used as a robust predictive model order reduction tool for nonlinear dynamical systems.
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USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
SC0019290
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2019.04.025