This talk will provide a high level overview of my PhD research, which has been focused on developing and applying reduced models for turbulence. It will be separated into two parts; (1) developing a physics informed machine learning approach for obtaining reduced Lagrangian models, and (2) extending the data-driven Mori-Zwanzig formalism for extracting spatio-temporal coherent structures from nonlinear dynamical systems.

Part 1 We blend modern machine learning techniques with Smoothed Particle Hydrodynamics (SPH: a mesh-free Lagrangian numerical scheme for solving PDEs) to discover optimal reduced Lagrangian models for turbulence. We compare a hierarchy of parameterizations of SPH, mixing Neural network and physics based parameters, measuring generalization errors over different resolutions, turbulent Mach numbers, and time scales. Some ongoing and future work will be discussed.

Part 2 We introduce the Mori-Zwanzig Modal Decomposition (MZMD); a novel technique for performing modal analysis of large-scale spatio-temporal structures in nonlinear dynamical systems. We show several comparisons of MZMD to Dynamic Mode Decomposition (DMD); (1) the theoretical relationship, (2) MZMD improves future state prediction accuracy, especially in strongly nonlinear regions, (3) each require nearly the same computational cost, (4) and MZMD can capture transient dynamics. We will conclude with some ongoing and future work.

The speaker will be on Zoom:  https://arizona.zoom.us/j/87333399931 

(no password)