Related papers: Rethinking Forward Processes for Score-Based Nonli…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…
Data assimilation methods aim at estimating the state of a system by combining observations with a physical model. When sequential data assimilation is considered, the joint distribution of the latent state and the observations is described…
Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…
Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a…
Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed…
The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of…
State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose…
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.…
In many engineering and applied science domains, high-dimensional nonlinear filtering is still a challenging problem. Recent advances in score-based diffusion models offer a promising alternative for posterior sampling but require repeated…
Data assimilation techniques are crucial for accurately tracking complex dynamical systems by integrating observational data with numerical forecasts. Recently, score-based data assimilation methods emerged as powerful tools for…
Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality,…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…
We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low…
Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…