Kernel-smoothed proper orthogonal decomposition-based emulation for spatiotemporally evolving flow dynamics prediction

This interdisciplinary study, which combines machine learning, statistical methodologies, high-fidelity simulations, projection-based model reduction, and flow physics, demonstrates a new process for building an efficient surrogate model to predict spatiotemporally evolving flow dynamics for design survey. In our previous work, a common proper-orthogonal-decomposition (CPOD) technique was developed to establish a physics-based surrogate (emulation) model for prediction of useful flow physics and design exploration over a wide parameter space. The emulation 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 large-scale 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 using high-fidelity simulation data, achieving a turnaround time for evaluating new design points that is 42,000 times faster than the original simulation.