Data assimilation combines observations and model predictions to improve our understanding and forecasting of evolving systems, making it an essential tool in fields like meteorology, climate science, and engineering. This approach treats time as a key variable, continually integrating incoming data into a model to adjust predictions and correct for uncertainty. In this tutorial, we will explore data assimilation as a type of time-dependent inverse problem by using concepts from dynamical systems and probability to reconstruct the state of a system from predictive models and observational data.
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