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Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be…

Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…

Despite the massive advancements in large language models (LLMs), they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict…

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Model updating of engineering systems inevitably involves handling both aleatory or inherent randomness and epistemic uncertainties or uncertainities arising from a lack of knowledge or information about the system. Addressing these…

How do we know how much we know? Quantifying uncertainty associated with our modelling work is the only way we can answer how much we know about any phenomenon. With quantitative science now highly influential in the public sphere and the…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks result in local reductions in stiffness parameters and may drastically…

Computer vision leveraging deep learning has achieved significant success in the last decade. Despite the promising performance of the existing deep models in the recent literature, the extent of models' reliability remains unknown.…

In this paper we propose a numerical procedure for the quantification of uncertainties in wave-structure interaction. We utilise the smoothed particle hydrodynamics (SPH) scheme for modelling the wave mechanics, coupled one-way with a…

A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification…

Due to the penetration of renewable energy resources and load deviation, uncertainty handling is one of the main challenges for power system; therefore the need for accurate decision-making in a power system under the penetration of…