Data Assimilation for dynamical systems and machine learning

We commonly refer to state estimation theory in geosciences as data assimilation (DA). This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical information (such as a dynamical evolution model), provides an estimate of its state. DA is standard practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean, and environment modeling; in all circumstances where one intends to estimate the state of a large dynamical system based on limited information. While the complexity of DA, and of the methods thereof, stands on its interdisciplinary nature across statistics, dynamical systems, and numerical optimization, when applied to geosciences, an additional difficulty arises by the continually increasing sophistication of the environmental models.  

Our group works on both the theoretical development of novel DA methods, at the crossroad between applied mathematics, dynamical systems, and machine learning, as well as their application to an ample range of applications in the climate science area. The latter includes, but are not limited to, meteorology, hydrology, sea-ice, and ocean. 

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

In recent years, the discipline has been influenced by the rapid advent of artificial intelligence, in particular machine learning (ML), 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. An example is the Scale Aware Sea-Ice Project (SASIP) in which our group coordinates the activities in data assimilation and machine learning.