Kernel-smoothed proper orthogonal decomposition (KSPOD)-based emulation for prediction of spatiotemporally evolving flow dynamics

1 Kernel-smoothed proper orthogonal decomposition (KSPOD)-based emulation for prediction of spatiotemporally evolving flow dynamics Yu-Hung Chang a,*, Liwei Zhang a,**, Xingjian Wang a,†, Shiang-Ting Yeh a,††, Simon Mak b,‡, Chih-Li Sung b,‡, C. F. Jeff Wu b, §, Vigor Yang a, ¶ a School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA b School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA* Abstract This interdisciplinary study, which combines machine learning, statistical methodologies, highfidelity simulations, and flow physics, demonstrates a new process for building an efficient surrogate model for predicting spatiotemporally evolving flow dynamics. In our previous work, a common-grid proper-orthogonal-decomposition (CPOD) technique was developed to establish a physics-based surrogate (emulation) model for prediction of mean flowfields and design exploration over a wide parameter space. The CPOD technique is substantially improved upon here using a kernel-smoothed POD (KSPOD) technique, which leverages kriging-based weighted functions from the design matrix. The resultant emulation model is then trained using a dataset obtained through high-fidelity simulations.