Chin. Phys. B, 2021, Vol. 30(3): 030204    DOI: 10.1088/1674-1056/abd92e
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Constructing reduced model for complex physical systems via interpolation and neural networks

Xuefang Lai(赖学方), Xiaolong Wang(王晓龙)†, and Yufeng Nie(聂玉峰)
1 Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China
Abstract  The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate the nonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic mode decomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy. Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.
Keywords:  model reduction      discrete empirical interpolation method      dynamic mode decomposition      neural networks
Received:  12 November 2020      Revised:  17 December 2020      Accepted manuscript online:  07 January 2021
 PACS: 02.30.Jr (Partial differential equations) 02.60.Cb (Numerical simulation; solution of equations) 02.60.Gf (Algorithms for functional approximation)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11871400 and 11971386) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2017JM1019).
Corresponding Authors:  Corresponding author. E-mail: xlwang@nwpu.edu.cn

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