Title: Vector-Valued Spectral Analysis of Complex Flows

Biography:

Joanna has a comprehensive multidisciplinary background, including a Masters degree in Physics with a focus on theoretical astrophysics and stellar pulsations, a PhD in Computational Fluid Dynamics for geophysical flows, and postdoctoral research training in Applied Mathematics. Joanna is a postdoctoral associate working on a range of topics, from theoretical development of data-driven methods for dynamical systems, to their subsequent application to various fields of physics. In particular, the current focus of her work is on machine learning techniques for analysis of spatiotemporal patterns of ultrafast spectroscopical data, complex turbulent flows, and more to come.

Abstract

We apply a recently developed framework for spatiotemporal pattern extraction called Vector-Valued Spectral Analysis (VSA). This approach is based on the eigendecomposition of a kernel integral operator acting on vector-valued observables (spatially extended fields) of the dynamical system generating the data, constructed by combining elements of the theory of operator-valued kernels for multitask machine learning with delay-coordinate maps of dynamical systems. A key aspect of this method is that it utilizes a kernel measure of similarity that takes into account both temporal and spatial degrees of freedom (whereas classical techniques such as EOF analysis are based on aggregate measures of similarity between “snapshots”). As a result, VSA has high skill in extracting physically meaningful patterns with intermittency in both space and time, while factoring out any symmetries present in the data. We demonstrate the efficacy of this method with applications to various cases of complex turbulent flows.