Large deviations and statistical inference in phased materials

I gave a talk at the AMS Western Sectional in the following special session: PDEs, Data, and Inverse Problems. The meeting was hosted by the University of Utah. Many thanks to Vincent R Martinez for inviting me.

Abstract:

Physical systems and the partial differential equations used to model them often exhibit dynamical regimes with distinct qualitative behaviour, called phases. Understanding how such regimes arise is important to understanding features of complexity in physics, and to making physical sense of the low-dimensional or asymptotic behaviours of many PDEs. We propose a Lyapunov function inspired by statistical inference that describes phase occupation in probabilistic terms. This defines a large deviations principle that makes our framework valid outside of equilibrium, and extends it beyond the usual notion of a Landau phase. Importantly, we recover from this an inference algorithm which extracts the microscopic dynamics of order parameters that correspond to macroscopic observations of phases.

Slides: AMS October 2022

Other details: link to website