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Title: Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

Abstract

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1557890
Alternate Identifier(s):
OSTI ID: 1559605
Grant/Contract Number:  
AC05-00OR22725; ERKJ314
Resource Type:
Published Article
Journal Name:
Mathematics
Additional Journal Information:
Journal Volume: 7; Journal Issue: 8; Journal ID: ISSN 2227-7390
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; reduced-order model; fluid dynamics; neural network; multistep method; optimization

Citation Formats

Xie, Xuping, Zhang, Guannan, and Webster, Clayton G. Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network. United States: N. p., 2019. Web. doi:10.3390/math7080757.
Xie, Xuping, Zhang, Guannan, & Webster, Clayton G. Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network. United States. doi:10.3390/math7080757.
Xie, Xuping, Zhang, Guannan, and Webster, Clayton G. Mon . "Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network". United States. doi:10.3390/math7080757.
@article{osti_1557890,
title = {Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network},
author = {Xie, Xuping and Zhang, Guannan and Webster, Clayton G.},
abstractNote = {In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.},
doi = {10.3390/math7080757},
journal = {Mathematics},
number = 8,
volume = 7,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.3390/math7080757

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