  This interdisciplinary study, which combines machine learning, statistical
methodologies, high-fidelity 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. As an example, the flow evolution in a swirl
injector is considered for a wide range of design parameters and operating
conditions. The KSPOD-based emulation model performs well, and can faithfully
capture the spatiotemporal flow dynamics. The model enables effective design
surveys utilizing high-fidelity simulation data, achieving a turnaround time
for evaluating new design points that is 42,000 times faster than the original
simulation.
