Emilia Magnani

Learning differential equations is an emerging research theme in machine learning. Differential equations are interesting because they offer a powerful language for dynamical relationships between variables and a mechanism for reduction for structured models, which is especially relevant in science. The project will explore two key functionalities in the context of machine learning for dynamical systems: Learning to solve differential equations by directly inferring the solution operator (Green’s function), and solving inverse problems (i.e. inferring the differential equation from observed solutions). A particular focus will be on notions of error and uncertainty. We will aim to extend recently developed frameworks in a Bayesian fashion, as well as to theoretically analyse these methods to establish convergence or failure modes.