Data assimilation combines the state of a model with incoming data by solving an
inverse problem to balance the uncertainty between them. Data assimilation is
used in applications from computer vision and remote sensing to weather
forecasting. Physical models are formulated as partial differential equations,
which have solutions in spaces of functions.
Their discretization leads to high-dimensional problems, and uncertainty can be
modeled by stochastic ensembles of simulations. The lecture will discuss the
principles of data assimilation with infinitely dimensional state and data, and
show the convergence of the ensemble Kalman filter with increasing ensemble size
independently of the state and data dimensions, including infinite dimension.