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 approxima...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 accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.展开更多
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).
文摘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 accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.
