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Machine learning techniques have seen a tremendous rise in popularity in weather and climate sciences. Data assimilation (DA), which combines observations and numerical models, has great potential to incorporate machine learning and…

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…

Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…

Deep neural networks (DNNs) are often coupled with physics-based models or data-driven surrogate models to perform fault detection and health monitoring of systems in the low data regime. These models serve as digital twins to generate…

A dynamic weighted directed graph (DWDG) is commonly encountered in various application scenarios. It involves extensive dynamic interactions among numerous nodes. Most existing approaches explore the intricate temporal patterns hidden in a…

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…

Wireless Sensor Network (WSN) localization refers to the problem of determining the position of each of the agents in a WSN using noisy measurement information. In many cases, such as in distance and bearing-based localization, the…

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for…

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an…

We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any…

The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering…

We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…

Predicting the evolution of turbulent flows is central across science and engineering. Most studies rely on simulations with turbulence models, whose empirical simplifications introduce epistemic uncertainty. The Eigenspace Perturbation…

Deep learning (DL) models have received particular attention in medical imaging due to their promising pattern recognition capabilities. However, Deep Neural Networks (DNNs) require a huge amount of data, and because of the lack of…

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually…

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning…

The Koopman Operator (KO) provides an analytical solution of dynamical systems in terms of orthogonal polynomials. This work exploits this representation to include the propagation of uncertainties, where the polynomials are modified to…

Nowadays, with the development of multi-sensor networks, the distributed cubature Kalman filter is one of the well-known existing schemes for state estimation, for which the influence of the non-Gaussian noise, abnormal data, and…

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…