CMX Lunch Seminar

Data assimilation aims to reconstruct the state of a dynamical system by combining partial observations with a mathematical model. For fluid flows governed by the incompressible Navier-Stokes equations, classical results show that coarse observations distributed across the entire spatial domain can recover the full flow through continuous nudging, known as the Azouani-Olson-Titi 2014 algorithm. In practice, however, sensor placement is often limited, and efficient reconstruction of turbulent flows requires strategic positioning of available measurements.

In this talk, we challenge the standard framework by showing that it is possible to recover the full system dynamics using only local observations from a subregion of the domain. In particular, we demonstrate that achieving global accuracy does not necessarily require global data: carefully chosen localized observations can be sufficient to synchronize the model with the true flow. This naturally raises a fundamental question: given a physical domain, should the observational region be placed near the boundary or away from it? We discuss recent theoretical results and numerical experiments that aim to shed light on this question.