Proper orthogonal decomposition and physical field reconstruction with artificial neural networks (ANN) for supercritical flow problems

Feng Sun, Gongnan Xie*, Jian Song, Christos N. Markides*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

The development of mathematical models, and the associated numerical simulations, are challenging in higher-dimensional systems featuring flows of supercritical fluids in various applications. In this paper, a data-driven methodology is presented to achieve system order reduction, and to identify important physical information within the principal flow features. Firstly, a new hybrid neural network based on radial basis function (RBF) and multi-layer perceptron (MLP) methods, namely RBF-MLP, is tested to achieve a highly nonlinear approximation. When provided with 1000 nonlinear test samples, this model provides an excellent prediction accuracy with a maximum regression coefficient (R) of 0.99 and a minimum root mean square error (RMSE) below 1%. Furthermore, the model is also proven to be flexible enough to capture accurately the turbulent fluctuation characteristics, even at significant nonlinear buoyancy conditions. Secondly, the high-dimensional buoyancy data is collected and integrated into a matrix database. Subsequently, a proper orthogonal decomposition (POD) approach is employed to reduce the high-dimensional database, and to obtain a set of low-dimensional POD basis-spanned space, which defines a reduced-order system with low-dimensional basis vectors. The results reveal that the first five order modes contain dominant flow features, accounting for 93% of the total mode energy, which can be selected to reconstruct the physical flow field. Thirdly, a new data-driven POD-ANN model is established to construct the nonlinear mapping between the full-field buoyancy data and decomposed basis vectors. It is also demonstrated that the POD-ANN model reconstructs the principal flow features accurately and reliably. This POD-ANN model can be used to provide new insights for reduced-order modelling and for reconstructing physical fields of higher-dimensional nonlinear flow cases.

Original languageEnglish
Pages (from-to)282-299
Number of pages18
JournalEngineering Analysis with Boundary Elements
Volume140
Early online date21 Apr 2022
DOIs
Publication statusPublished - Jul 2022

Bibliographical note

Funding Information:
This work was sponsored by the National Natural Science Foundation of China (51676163), the National 111 Project under Grant No. B18041, the Fundamental Research Funds for the Central Universities (3102020HHZY030005), Guangdong Basic and Applied Basic Research Foundation (2019A1515111146) and the Fundamental Research Funds of Shenzhen City (JCYJ20170306155153048). The work was also supported by Russian Government “Megagrant” project 075-15-2019-1888.

Publisher Copyright:
© 2022 Elsevier Ltd

Keywords

  • artificial neural network (ANN)
  • field construction
  • order reduction
  • proper orthogonal decomposition (POD)
  • supercritical fluid flows

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Computational Mathematics
  • Applied Mathematics

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