Research Area A – Theory and Algorithms

Research Area A focuses on the theoretical and algorithmic foundation of data assimilation. In case of a data-rich situation (e.g.~fully observed processes) and finite-dimensional estimation problems, there is a well-developed theory available. The situation changes fundamentally when one moves from such well-posed to ill-posed statistical inverse problems, i.e., towards partially observed processes and/or infinite-dimensional estimation problems (non-parametric statistics), where there are many open mathematical problems and algorithmic challenges.