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Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
We propose a new type of the Ensemble Kalman Filter (EnKF), which uses the Fast Fourier Transform (FFT) for covariance estimation from a very small ensemble with automatic tapering, and for a fast computation of the analysis ensemble by…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
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…
This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime,…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
Coastal flooding poses increasing threats to communities worldwide, necessitating accurate and hyper-local inundation forecasting for effective emergency response. However, real-world deployment of forecasting systems is often constrained…
Image inpainting is a technique used to restore missing or damaged regions of an image. Traditional methods primarily utilize information from adjacent pixels for reconstructing missing areas, while they struggle to preserve complex details…
The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…
Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and…
We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an…
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations…
In this paper, we propose and develop a methodology for nonlinear systems health monitoring by modeling the damage and degradation mechanism dynamics as "slow" states that are augmented with the system "fast" dynamical states. This…
The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…
Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary…
Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only…
Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it…
Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…