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Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
High-resolution temperature monitoring is essential for many engineering and scientific applications, but conventional sensors are limited by insufficient resolution and susceptibility to electromagnetic interference. Fiber-optic…
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…
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…
We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
Understanding human motion is of critical importance for health monitoring and control of assistive robots, yet many human kinematic variables cannot be directly or accurately measured by wearable sensors. In recent years, invariant…
We present a novel sampling-based method for estimating probabilities of rare or failure events. Our approach is founded on the Ensemble Kalman filter (EnKF) for inverse problems. Therefore, we reformulate the rare event problem as an…
The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the…
A data-driven investigation of the flow around a high-rise building is performed combining heterogeneous experimental samples and RANS CFD. The coupling is performed using techniques based on the Ensemble Kalman Filter (EnKF), including…
This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…
Compressed Estimation approaches, such as the Generalised Compressed Kalman Filter (GCKF), reduce the computational cost and complexity of high dimensional and high frequency data assimilation problems; usually without sacrificing…
Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are…
This work introduces a new, distributed implementation of the Ensemble Kalman Filter (EnKF) that allows for non-sequential assimilation of large datasets in high-dimensional problems. The traditional EnKF algorithm is computationally…
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction…
Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…
Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in…