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

作     者：Xuefang Lai Xiaolong Wang Yufeng Nie 赖学方;王晓龙;聂玉峰

作者机构：Research Center for Computational ScienceSchool of Mathematics and StatisticsNorthwestern Polytechnical UniversityXi’an 710129China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2021年第30卷第3期

页      面：78-87页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070201[理学-理论物理] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11871400 and 11971386) the Natural Science Foundation of Shaanxi Province,China(Grant No.2017JM1019) 

主　　题：model reduction discrete empirical interpolation method dynamic mode decomposition neural networks 

摘      要：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 thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction ***, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.