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Learning to solve Differential Equations with Uncertainty

Emilia Magnani (Ph.D. Student)

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.

Primary Host: Philipp Hennig (University of Tübingen)
Exchange Host: Lorenzo Rosasco (University of Genoa, Italian Institute of Technology & Massachusetts Institute of Technology)
PhD Duration: 01 December 2020 - 30 November 2023
Exchange Duration: 01 December 2021 - 28 February 2022 01 December 2022 - 28 February 2023