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

Xuping Xie, Guannan Zhang and Clayton G. Webster
Additional contact information
Xuping Xie: Computation and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Guannan Zhang: Computation and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Clayton G. Webster: Computation and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Mathematics, 2019, vol. 7, issue 8, 1-15

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.

Keywords: reduced-order model; fluid dynamics; neural network; multistep method; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/8/757/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/8/757/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:8:p:757-:d:258869

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().