Data assimilation combines control theory and scientific computing to propose a set of
methods for coupling dynamic models and data sequences for estimation and prediction in …

To understand and predict the behavior of a system one can use measurements or one can
develop physically based numerical models. In many applications however neither of these …

The principles of optimal control of distributed parameter systems are used to derive a
powerful class of numerical methods for solutions of inverse problems, called data …

A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …

We present a new continuous data assimilation algorithm based on ideas that have been
developed for designing finite-dimensional feedback controls for dissipative dynamical …

The process of integrating observations into a numerical model of an evolving dynamical
system, known as data assimilation, has become an essential tool in computational science …

The bulk of this paper contains a concise mathematical overview of the subject of data
assimilation, highlighting three primary ideas:(i) the standard optimization approaches of …

Data assimilation is a method that combines observations (ie, real world data) of a state of a
system with model output for that system in order to improve the estimate of the state of the …

Dynamic data assimilation is the assessment, combination and synthesis of observational
data, scientific laws and mathematical models to determine the state of a complex physical …

This paper considers continuous data assimilation (CDA) in partial differential equation
(PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove …