Related papers: Almost sure error bounds for data assimilation in …
Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data…
In using data assimilation to import information from observations to estimate parameters and state variables of a model, one must assume a distribution for the noise in the measurements and in the model errors. Using the path integral…
Using a dynamical model to make predictions about a system has many sources of error. These can include errors in how the model was initialised but also errors in the dynamics of the model itself. For many applications in data assimilation,…
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…
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
4D-variational data assimilation is applied to the Lorenz '63 model to introduce a new method for parameter estimation in chaotic climate models. The approach aims to optimise an Earth system model (ESM), for which no adjoint exists, by…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
This paper considers the ill-posed data assimilation problem associated with hyperbolic/parabolic systems describing 2D coupled sound and heat flow. Given hypothetical data at time T > 0, that may not correspond to an actual solution of the…
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…
Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…
In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a…
Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…
This paper focuses on continuous data assimilation (CDA) for the Navier-Stokes equations with nonlinear slip boundary conditions. CDA methods are typically employed to recover the original system when initial data or viscosity coefficients…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…
An algorithm for continuous data assimilation for the two- dimensional B\'enard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier-Stokes equations, which allows for the…
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the…