IAPPS

Information Assimilation in Probabilistic PDE Simulation

01/06/2024 to 31/05/2027

Probabilistic simulation methods have recently emerged as a novel, data-centric paradigm at the intersection of simulation and inference. The probabilistic viewpoint provides a principled way to encode structural knowledge about a problem. By giving an explicit role to uncertainty from all sources, probabilistic numerics gives rise to new applications beyond the scope of classical methods. For ordinary differential equations, probabilistic solvers now match the runtime of classical methods, despite their improved functionality. For partial differential equations (PDEs), promising early results exist, but further improvements are necessary. The aim of this project will be to apply this probabilistic framework to PDEs. In particular, we will focus on PDEs on non-Euclidean geometries, such as fluid dynamics simulations on the sphere. The resulting method will thus, in particular, provide novel functionality for climate and weather models.