Data and Models
Modern data acquisition technologies offer a wealth of information that is more and more used towards enhancing accuracy and prediction capability of classical mathematical models as well as learning improved or even new models.
Properly synthesizing "model based" and "data driven" methodologies is therefore a key objective at the interface of numerical analysis, scientific computing, and data science.This talk addresses some fundamental mathematical aspects of Uncertainty Quantification, in the context of forward and inverse tasks like data assimilation, parameter and state estimation. In particular, we highlight the role of reduced models. Key issues concern their certifiability based on suitable variational formulations of the underlying continuous model as well as some intrinsic obstructions due to the inherently high dimensional nature of related recovery tasks. We discuss some remedies combining deterministic and probabilistic techniques and demonstrate possible merits of nonlinear versus linear reduced modeling.