Non-intrusive inference reduced order model for fluids using deep multistep neural network

Xuping Xie, Guannan Zhang, Clayton G. Webster

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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.

Original languageEnglish
Article number757
JournalMathematics
Volume7
Issue number8
DOIs
StatePublished - Aug 1 2019

Bibliographical note

Publisher Copyright:
© 2019 by the authors.

Keywords

  • Fluid dynamics
  • Multistep method
  • Neural network
  • Optimization
  • Reduced-order model

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