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.

提出了一种改进的数据驱动的非侵入式模型降阶 (MOR) 方法，该方法能够针对参数对瞬态流场和其他类型的数据进行插值。建议的 MOR 方法包括以下两个阶段：MOR 和插值。对于 MOR，使用改进的适当正交分解 (POD) 来收集参数独立的 POD 模式和相关系数。POD 系数的插值是通过无监督机器学习进行的，称为 Wasserstein 生成对抗网络梯度惩罚 (WGAN-GP)。通过使用深度卷积神经网络，WGAN-GP 稳定了跨参数的插值，并确保在参数空间内几乎没有结果的准确插值。然后使用参数内插的 POD 系数和相关的独立模式生成内插对象。接下来，应用围绕静止圆柱体和俯冲翼型的流场来证明所提出方法的效率和准确性，并评估 POD 模式和参数对准确性的影响。最后，通过采用准确度指标将准确度和效率与其他方法进行比较。基于结果，发现所提出的方法对于对象插值是有效且高效的。并评估了POD模式和参数对精度的影响。最后，通过采用准确度指标将准确度和效率与其他方法进行比较。基于结果，发现所提出的方法对于对象插值是有效且高效的。并评估了POD模式和参数对精度的影响。最后，通过采用准确度指标将准确度和效率与其他方法进行比较。基于结果，发现所提出的方法对于对象插值是有效且高效的。