When
Where
Speaker: Michael Woodward, Postdoctoral Researcher, Los Alamos National Laboratory
Title: Reduced order models: Lagrangian and Mori-Zwanzig methods
Abstract: Many naturally occurring phenomena, such as turbulent flows, can be characterized as high-dimensional nonlinear dynamical systems that exhibit strong coupling across a broad range of scales. In contrast to simulating the dynamics over all relevant scales, reduced-order models seek to describe the dynamics using a low-dimensional space of variables, referred to as "resolved variables" or observables. ROMs can be used to simulate the dynamics at substantially reduced computational costs as well as provide tractable frameworks for analyzing and understanding the underlying physics. The main challenge of developing reduced models, such as those required in turbulence, is in their ability to generalize; for example, over different Reynolds and Mach numbers.
In this talk I will cover two approaches to develop data-driven models for hydrodynamic applications. In the first I will present a parameterized Smoothed Particle Hydrodynamics model for a turbulent, and compressible flows. Next, we will look at the data-driven Mori-Zwanzig method as an extension of Dynamic Mode Decomposition. I will also discuss some open problems and future directions.