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Gaussian Random Fields (GRFs) with Mat\'ern covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness…
Data assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields,…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
High-fidelity simulations are essential for predicting material behavior under high-velocity impact (HVI), but their accuracy depends on material models and parameters that are often calibrated by manual fitting to multiple costly…
Power system dynamic state estimation is essential to monitoring and controlling power system stability. Kalman filtering approaches are predominant in estimation of synchronous machine dynamic states (i.e. rotor angle and rotor speed).…
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…
Owing to advances in data assimilation, notably Ensemble Kalman Filter (EnKF), flood simulation and forecast capabilities have greatly improved in recent years. The motivation of the research work is to reduce comprehensively the…
Score matching estimators have garnered significant attention in recent years because they eliminate the need to compute normalizing constants, thereby mitigating the computational challenges associated with maximum likelihood estimation…
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…
This paper presents an innovative Reduced-Order Model (ROM) for merging experimental and simulation data using Data Assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and…
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…
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The…
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…
The probability prediction of multivariate time series is a notoriously challenging but practical task. On the one hand, the challenge is how to effectively capture the cross-series correlations between interacting time series, to achieve…
This paper presents a model-based method for fusing data from multiple sensors with a hypothesis-test-based component for rejecting potentially faulty or otherwise malign data. Our framework is based on an extension of the classic particle…
A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…
Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…
Delay-and-sum (DAS) algorithms are widely used for beamforming in linear array photoacoustic imaging systems and are characterized by fast execution. However, these algorithms suffer from various drawbacks like low resolution, low contrast,…