Applied Mathematics Seminar | Daniel Messenger, Weak-form equation learning with applications to cell migration and general multiscale phenomena

MC 5501 

Speaker

Daniel Messenger, University of Colorado Boulder 

Title

Weak-form equation learning with applications to cell migration and general multiscale phenomena

Abstract

Equation learning has arisen as a paradigm for constructing governing equations for phenomena of interest using observations of the underlying system. In the context of differential equations, a consensus has formed that weak-form equation learning (WFEL) offers many advantages, such as implicit noise filtering, high accuracy, and reduced regularity requirements on the ground-truth data. In this talk I will review essential components of the WSINDy algorithm (Weak-form Sparse Identification of Nonlinear Dynamics) to demonstrate these advantages in the discovery of ordinary and partial differential equations. I will also delve into a new paradigm for which WFEL appears to be particularly well-suited, that of inference for multiscale systems. Recent works have shown that WSINDy can aid in the discovery of interpretable mean-field laws for large systems of particles, homogenization of highly-oscillatory media, and coarse-graining of Hamiltonian systems with approximate symmetries. I will survey these results and with applications to cell migration experiments, and provide a general outlook for this line of research.