A real-time variational data assimilation method based on complexity reduction and on-the-fly data-driven empirical enrichment

State estimation is a specific data assimilation task in which the quantity of interest is the state of the physical system over a domain of interest. For that purpose, we rely on observations on the system, given by sensors at different sampling times, and a best-knowledge model. However, how good the model may be, it is a deficient representation of the true physics, it may lack some not modeled physics, or parameter values can be inaccurate and erroneous. Therefore, the model bias affects the effectiveness of data assimilation techniques and needs to be corrected with observation data. Moreover, for several years, the explosion of the access to experimental data in industrial systems and the considerable improvements in computing tools have led to the development of data assimilation methods that aim to be used for system monitoring with a real-time constraint. The first idea to decrease the computational cost in the online procedure is to use reduced order modeling (ROM) methods, indeed the reduction of the complexity of the model can overcome the difficulties at the cost of controlling and integrating the model error.