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Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Ito process. This work…
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 methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
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.…
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
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…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…
The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…
In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to…
This paper studies whether numerically preserving monotonic properties can offer modelling advantages in data assimilation, particularly when the signal or data is a realization of a stochastic partial differential equation (SPDE) or…
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…
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 goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
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…
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…
Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…