PhD scholarship in dynamical systems and operator learning

I am offering a PhD scholarship in dynamical systems and operator learning, as part of
the DECRA project "From chaos to clarity: reliable data-driven analysis of dynamical
systems".  

The link to apply is at
https://www.sydney.edu.au/scholarships/d/arc-postgraduate-research-scholarship.html 

The scholarship is open to both domestic and international applicants.  Feel free to
share this with anyone who might be interested.  

Project title: Developing error quantification of Koopman operator algorithms 

Project summary: In scientific applications, many interesting dynamical systems are
governed by equations that are unknown to use.  We would like to predict them and study
their emergent behaviour, but we may only have a limited amount of observations to work
with.  Various tools exist that facilitate this up to some error, most of which involve
approximating these systems' Koopman operator.  The Koopman operator is a linear
operator on functions that encodes composition by the dynamics and whose eigenfunctions
reveal emergent patterns.  For many chaotic systems, the stability of the approximated
Koopman operator can be highly variable depending on what is being measured.  This makes
error quantification very important in applications.  This project will develop
mathematically rigorous error quantification for a kernel-based algorithm known as
kernel Extended Dynamical Mode Decomposition.  We will seek to quantitatively understand
how least-squares approximation affects the spectrum of infinite-dimensional operators,
and develop indicators and statistical tests to measure this.  This will involve
applying, and where needed developing, rigorous approximation theory and probability
theory in the context of dynamical systems.  A strong mathematical background with at
least one of functional analysis or probability theory would be desirable.