A 3-D Kinetic-Based Discrete Dynamic System and its Surrogate Models by Machine Learning

Naiver-stokes based discrete dynamical system (DDS) has been used in turbulence modeling to capture the subgrid-scale motion. We have recently derived a 3-D DDS for incompressible flows based on the kinetic-based lattice Boltzmann equation (LBE). Five bifurcation parameters, including a relaxation time from the LBE, a splitting factor to separate large-scale and sub-grid scale (SGS) motion, and three wavevector components from the Fourier space Galerkin procedure used to derive the DDS. Numerical experiments employing combinations of these bifurcation parameters have produced laminar and turbulent flow behaviors indicated by the patterns of power spectral density (PSD) of the time series. To use this DDS for generating SGS information in large-eddy simulation (LES) of pulsatile turbulence via the lattice Boltzmann method, we intend to systematically study the effects of the bifurcation parameters on capturing laminar and turbulence behaviors. To overcome the demands of computation time, we developed surrogate models for the DDS through physics-based machine learning classification techniques including Support Vector Machines and Artificial Neural Networks. The surrogate models from both machine learning methods result in prediction precision varying from 93% to 99% based on the size of test point sets. For 15,000 test points, the surrogate models reduce 98% of computation time to the DDS. We will use the surrogate models to explore phase diagrams in the 5-dimensioanl parameter space, which will be critically important for appropriately selecting bifurcation parameters for LES modeling of pulsatile turbulence.