Data Assimilation for dynamical systems and machine learning

Data assimilation (DA) refers to the entire sequence of operations that, from the observations of a system, and additional statistical and dynamical information, provides an estimate of its state. DA is crucial in numerical weather prediction, but its application is widespread in many other areas of climate science; whenever one intends to estimate the state of a large dynamical system based on limited information. The complexity of DA, and its beauty, stands on its interdisciplinary nature across statistics, dynamical systems, and numerical optimization. 

We work on theoretical developments, at the crossroad between applied mathematics, dynamical systems, and machine learning (ML), and on applications to an ample range of problems in meteorology, hydrology, sea-ice, and ocean.

The figure illustrates the different DA methods depending on the spatial resolution and on the desired forecast horizon, together with a schematic of the diverse climate phenomena (from Carrassi et al., 2018).

In recent years, the discipline has been influenced by the rapid advent of artificial intelligence, opening the path to the explosion of a rich offer of hybrid methods between DA and ML. Our group is also at the forefront of this transition, producing innovative results and participating in several international research efforts.