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Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…
There is growing interest in data-driven weather prediction (DDWP), for example using convolutional neural networks such as U-NETs that are trained on data from models or reanalysis. Here, we propose 3 components to integrate with commonly…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
This paper introduces an extension of generalised filtering for online applications. Generalised filtering refers to data assimilation schemes that jointly infer latent states, learn unknown model parameters, and estimate uncertainty in an…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one…
Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under…
In this paper, we derive a new Kalman filter with probabilistic data association between measurements and states. We formulate a variational inference problem to approximate the posterior density of the state conditioned on the measurement…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
The Extended Kalman Filter (EKF) is both the historical algorithm for multi-sensor fusion and still state of the art in numerous industrial applications. However, it may prove inconsistent in the presence of unobservability under a group of…
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…
In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman…
Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting…
Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance…
Continuously tracking the movement of a fluid or a plume in the subsurface is a challenge that is often encountered in applications, such as tracking a plume of injected CO$_2$ or of a hazardous substance. Advances in monitoring techniques…
The paper presents experiments of driving a physics-based thermosphere model by assimilating electron density (Ne) and temperature (Tn) data using the ensemble adjustment Kalman filter (EAKF) technique. This study not only helps to gauge…
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…