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Through ensemble-based data assimilation (DA), we address one of the most notorious difficulties in phase-resolved ocean wave forecast, regarding the deviation of numerical solution from the true surface elevation due to the chaotic nature…

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…

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…

Flood simulation and forecast capability have been greatly improved thanks to advances in data assimilation (DA) strategies incorporating various types of observations; many are derived from spatial Earth Observation. This paper focuses on…

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…

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…

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

We propose a regularization method for ensemble Kalman filtering (EnKF) with elliptic observation operators. Commonly used EnKF regularization methods suppress state correlations at long distances. For observations described by elliptic…

Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To reduce uncertainty and accelerate posterior inference, a…

The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…

Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable methods of MCMC are computationally expensive.…

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates…

An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation…

This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…

We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…