Related papers: Data Assimilation by Conditioning on Future Observ…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

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…

In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…

A modelling framework, based on the theory of signal processing, for characterising the dynamics of systems driven by the unravelling of information is outlined, and is applied to describe the process of decision making. The model input of…

Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

In order to evaluate and compare different recursive filters, simulation is a common tool and numerous simulation models are widely used as 'benchmark'. In the simulation, the continuous time dynamic system is converted into a discrete-time…

Data-driven learning is generalized to consider history-dependent multi-fidelity data, while quantifying epistemic uncertainty and disentangling it from data noise (aleatoric uncertainty). This generalization is hierarchical and adapts to…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…

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…

This paper considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data is streaming frequently while trying to reach a decision. Thus, we aim to devise a…

Inspired by the use of random projections in biological sensing systems, we present a new algorithm for processing data in classification problems. This is based on observations of the human brain and the fruit fly's olfactory system and…

Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future…