Seminar: Learning what tickles your flow from data

Benjamin Herrmann
Research Associate
Department of Mechanical Engineering at University of Washington
Institute of Fluid Mechanics at Technische Universität Braunschweig

Abstract
Many fluid flows behave as selective amplifiers of external disturbances –where most perturbations are damped out, a few favored excitation patterns lead to largely amplified responses. Resolvent analysis is a technique to identify these most-responsive forcings along with the corresponding most-amplified responses, based on the governing equations of the system. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, and to guide sensor/actuator placement for flow control applications.  However, resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this talk, I present the development of a purely data-driven algorithm to perform resolvent analysis to obtain the forcing and response modes of a linear system, without recourse to its governing equations, but instead based on snapshots of its transient evolution. The formulation of the method follows from two established facts: 1) dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and 2) a projection of the resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. I demonstrate the method on numerical data of the linearized complex Ginzburg–Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. The ability to perform resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to resolvent research and applications. Even with partial measurements and a limited dataset, experimental applications of data-driven resolvent analysis will enable learning high-gain input-output pairs of modes to provide valuable –and otherwise unavailable– information to guide controller design in non-normal systems.

About the speaker
Benjamin Herrmann is a DAAD PRIME fellow holding a double postdoctoral appointment working with Steven L. Brunton in the Department of Mechanical Engineering at University of Washington and with Richard Semaan in the Institute of Fluid Mechanics at TU Braunschweig. Benjamin received his B.S. and M.S. in mechanical engineering in 2014, and his Ph.D. in fluid dynamics in 2018 from University of Chile. His research combines machine learning methods with dynamical systems theory to model, understand and control complex systems for energy conversion applications.

Questions? Contact Asst. Prof. Zhuoyuan Song (UHM Mechanical Engineering; zsong@hawaii.edu)