Conference Agenda

Recent years have seen an explosive growth in the recording of increasingly complex and high-dimensional data. Classical statistical methods are often unfit to handle such data, whose analysis calls for the definition of new methods, merging ideas and approaches from statistics, applied mathematics and engineering. My talk will in particular focus on Physics-Informed statistical learning methods, which feature regularizing terms involving Partial Differential Equations (PDEs). Such PDEs encode the available problem-specific information about the phenomenon under study. The methods can handle spatial and functional data observed over non-Euclidean domains, such as linear networks, two-dimensional manifolds and non-convex volumes. The methods will be illustrated through applications from life and environmental sciences.