Non-Intrusive Parametric Reduced Order Models For The Prediction Of Internal And External Flow Fields Over Automobile Geometries

Abstract

Abstract In many-query applications such as design, optimization, and model-predictive control, reduced order models (ROMs) have the potential to significantly decrease the computational cost. In contrast to intrusive projection-based ROMs which require direct access to the high-fidelity model (HFM) operators, non-intrusive ROMs can be constructed in a data-driven fashion using the input-output data generated by the HFM. When used in the prediction of the system response in unseen parameter regimes, however, generalization capabilities have to be carefully assessed. In this study, we pursue a two-step approach to construct non-intrusive parametric ROMs: The first step involves the extraction of low-dimensional latent spaces using proper-orthogonal decomposition (POD) and convolutional neural network-based autoencoders (CNN-AE); and the second step uses regression for the latent variables in parameter space. We adapt a unique decomposition approach named Split-POD to enrich the low-dimensional subspace of the parametric ROM. The proposed methods are used to predict the flow field over a vehicle geometry as a function of vehicle speed and internal fan speed. Through orders of magnitude reduction in the degrees of freedom, the non-intrusive ROMs enable flow field prediction in real-time and bypass hours of computations by the HFM. The results show that the nonlinear encoding in CNN-AE can enhance ROM predictions given adequate data. POD-based ROMs are more robust and efficient, and in particular more accurate than CNN-AE in under-sampled regions of the parameter space. We further enhance the utility of non-intrusive ROMs by formulating a training process that minimizes the required number of high-fidelity simulations using Gaussian process regression to adaptively sample the input parameter space and optimize the estimated variance of the predictions.