Constructing reduced model for complex physical systems via interpolation and neural networks

doi:10.1088/1674-1056/abd92e

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

Cite this article:

Xuefang Lai(赖学方), Xiaolong Wang(王晓龙, and Yufeng Nie(聂玉峰) Constructing reduced model for complex physical systems via interpolation and neural networks 2021 Chin. Phys. B 30 030204

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