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The four-dimensional variational data assimilation (4D-Var) has emerged as an important methodology, widely used in numerical weather prediction, oceanographic modeling, and climate forecasting. Classical unconstrained gradient-based…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…
Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…
We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…
We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way this variational approach finds best estimates of the current state of the flow from a…
A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to…
An original graph clustering approach to efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here the localization term is very generic and refers to the idea of breaking up a…
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…
Earth system modeling presents a fundamental challenge in scientific computing: capturing complex, multiscale nonlinear dynamics in computationally efficient models while minimizing forecast errors caused by necessary simplifications. Even…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies developing novel schemes with an understanding of the rich…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…
Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many…
We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…
Data assimilation (DA) integrates observational data with numerical models to improve the prediction of complex physical systems. However, traditional DA methods often struggle with nonlinear dynamics and multi-scale variability,…