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A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing…

A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial…

Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric…

In order to achieve a more virtual design and certification process of jet engines in aviation industry, the uncertainty bounds for computational fluid dynamics have to be known. This work shows the application of a machine learning…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Accurate aircraft trajectory prediction (TP) in air traffic management systems is confounded by a number of epistemic uncertainties, dominated by uncertain meteorological conditions and operator specific procedures. Handling this…

Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…

A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory…

The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…

Weather forecasting requires not only accuracy but also the ability to perform probabilistic prediction. However, deterministic weather forecasting methods do not support probabilistic predictions, and conversely, probabilistic models tend…

Short-term forecasting is an important tool in understanding environmental processes. In this paper, we incorporate machine learning algorithms into a conditional distribution estimator for the purposes of forecasting tropical cyclone…

Advanced Aerial Mobility (AAM) operations require strategic flight planning services that predict both spatial and temporal uncertainties to safely validate flight plans against hazards such as weather cells, restricted airspaces, and CNS…

Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic…

Forecast systems in science and technology are increasingly moving beyond point prediction toward methods that produce full predictive distributions of future outcomes y, conditional on high-dimensional and complex sequences of inputs x.…

In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Bayesian inference is applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model. The model consists of cathode, discharge, and plume sub-models and outputs thruster performance metrics,…

We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system's evolution are accessible for various initial conditions, our goal is to infer…