Flow Prediction using Machine Learning based Reduced Order Models and Application to Shape Design Optimization

Abstract

Despite extensive research aimed at enhancing the efficiency of simulations in the field of CFD (Computational Fluid Dynamics), the computational cost of CFD remains a bottleneck, particularly in areas requiring iterative performance evaluations such as shape design. To overcome this limitation, recent studies have actively explored Reduced Order Modeling (ROM) techniques using machine learning. In many prior studies, unnecessary interpolation and mapping errors were introduced during the preprocessing of CFD data, compromising the advantages of high-order accuracy CFD solvers. Therefore, the first proposed methodology in this study employs a Conditional Unet based on Convolutional Neural Networks (CNNs). To avoid the occurrence of preprocessing errors, it directly applies structured grid based CFD data to training through a simple matrix transformation. Model validation involved flow field data from a transonic airfoil with varying shapes and flow conditions, and comparisons were conducted with the POD-GPR, a linear reduced order modeling technique, in terms of accuracy and efficiency. However, the proposed Conditional Unet still exhibits the limitation of being confined to structured grid data. To address this limitation, the second proposed methodology utilizes a point cloud format which independent of grid type, count, and topology. The introduced Local Point Encoding (LEP) layer transforms the point cloud into a format compatible with CNN operations, extending the applicability of existing CNN models while demonstrating robust characteristics against disparate training data formats. Model validation involved flow field data around a cylinder and an airfoil generated with unstructured grids, and comparisons were made with models from previous studies. Additionally, this study discusses the application of ROM to efficient shape design and inverse design techniques to illustrate examples of ROM utilization.