New Regularization Method for Calibrated POD Reduced-Order Models

Abstract

Reduced-order models based on Proper orthogonal decomposition are known to suffer from a lack of accuracy due to the truncation effect introduced by keeping only the most energetic modes. In this paper, we propose a new regularized calibration method aiming at minimizing a weighted average of normalized error, and a term measuring the change of the coefficients from their value obtained by Galerkin projection. We also determine the optimal value of the regularization parameter by analogy of the L-curve method. This paper is a sequel of [8] in which we compared various methods of calibration and introduced a Tikhonov-based regularization method. The proposed approach is assessed for a two dimensional wake flow around a cylinder, characteristic of the configurations of interest.

Keywords:

• POD reduced-order model
• regularization
• singular value decomposition
• L-curve
• optimization

AMS Subject Classification:

• 78M34
• 78M50
• 76F20
• 91A10