A0169
Title: Physics informed statistical learning for spatial and functional data
Authors: Laura Sangalli - Politecnico di Milano (Italy) [presenting]
Abstract: Physics-informed statistical learning methods are a new class of nonparametric and semiparametric regression models with roughness penalties. These methods can handle spatial and spatiotemporal data, as well as functional data, observed over multidimensional domains that can have complex shapes, such as non-convex planar domains, curved domains, non-convex volumes, and linear networks. By integrating differential operators, ranging from simple second derivatives and Laplacians to more sophisticated partial differential equations, these models leverage problem-specific knowledge to enhance model accuracy. The use of unstructured mesh discretization enables high modeling flexibility, making it possible to capture highly localized signals, strong anisotropies, and non-stationary patterns. The utility of these methods are illustrated through applications to complex data analysis problems from life and environmental sciences.
