Parametric non-intrusive model order reduction for flow-fields using unsupervised machine learning

Abstract

An improved data-driven non-intrusive model order reduction (MOR) methodology capable of interpolating time-transient flow-fields and other types of data with respect to the parameters is proposed. The proposed MOR method comprises the following two stages: MOR and interpolation. For the MOR, modified proper orthogonal decomposition (POD) is used to collect the parametrically independent POD modes and dependent coefficients. An interpolation of the POD coefficients is conducted through unsupervised machine learning, referred to as the Wasserstein generative adversarial network-gradient penalty (WGAN-GP). By using a deep convolutional neural network, WGAN-GP stabilizes the interpolation across the parameters and ensures an accurate interpolation with few results within the parametric space. An interpolated object is then generated using the parametrically interpolated POD coefficients and relevant independent modes. Next, flow-fields around a stationary cylinder and a plunging airfoil are applied to demonstrate the efficiency and accuracy of the proposed approach, and the influences of the POD modes and parameters on the accuracy are evaluated. Finally, the accuracy and efficiency are compared with those of other methods through the adoption of an accuracy index. Based on the results, the proposed method was found to be effective and efficient for object interpolation.