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Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…
We investigate the dynamic response of flexible aircraft in low-altitude atmospheric turbulence. To this end, three turbulence models of increasing fidelity, namely, the one-dimensional von K{\'a}rm{\'a}n model, the two-dimensional Kaimal…
Deep learning models are extensively used in various safety critical applications. Hence these models along with being accurate need to be highly reliable. One way of achieving this is by quantifying uncertainty. Bayesian methods for UQ…
Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…
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…
In order to understand underlying processes governing environmental and physical processes, and predict future outcomes, a complex computer model is frequently required to simulate these dynamics. However there is inevitably uncertainty…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…
High-fidelity computational simulations and physical experiments of hypersonic flows are resource intensive. Training scientific machine learning (SciML) models on limited high-fidelity data offers one approach to rapidly predict behaviors…
In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in…
Treating uncertainties in models is essential in many fields of science and engineering. Uncertainty quantification (UQ) on complex and computationally costly numerical models necessitates a combination of efficient model solvers, advanced…
The use of deep learning for medical imaging has seen tremendous growth in the research community. One reason for the slow uptake of these systems in the clinical setting is that they are complex, opaque and tend to fail silently. Outside…
Reliable wildfire spread prediction is vital for risk-aware emergency planning, yet most deep learning models lack principled uncertainty quantification (UQ). Further, for boundary-sensitive cases like wildfire spread, evaluating models…
Uncertainty quantification of the photogrammetry process is essential for providing per-point accuracy credentials of the point clouds. Unlike airborne LiDAR, whose accuracy generally remains consistent with objects with varying geometric…
Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to…
Turbulent flow has been extensively studied using computational fluid dynamics (CFD) simulations since turbulent flow regime is so frequently encountered in both academic and engineering applications. The high-fidelity simulation of the…
The presence of two-dimensional coherent structures in the near-field of the round jet has been established by several experimental investigations and direct Navier-Stokes simulations (DNS). Their study has a great importance to improve the…
In this paper, we present an approach for quantifying the propagated uncertainty of robot systems in an online and data-driven manner. Especially in Human-Robot Collaboration, keeping track of the safety compliance during run time is…
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…