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Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for…

Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…

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…

Aggregating data is fundamental to data analytics, data exploration, and OLAP. Approximate query processing (AQP) techniques are often used to accelerate computation of aggregates using samples, for which confidence intervals (CIs) are…

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…

Conformal prediction (CP) provides a framework for constructing prediction sets with guaranteed coverage, assuming exchangeable data. However, real-world scenarios often involve distribution shifts that violate exchangeability, leading to…

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. Most of these models involve inherent uncertainties that must be assessed to increase the confidence in model predictions…

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by…

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…

This paper introduces the first quantum computing framework for Stochastic Quantum Power Flow (SQPF) analysis in power systems. The proposed method leverages quantum states to encode power flow distributions, enabling the use of Quantum…

Measuring fluctuations in matter's low energy excitations is the key to unveil the nature of the nonequilibrium response of materials. A promising outlook in this respect is offered by spectroscopic methods that address matter fluctuations…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

While Deep Neural Networks (DNNs) achieve state-of-the-art accuracy in various applications, they often fall short in accurately estimating their predictive uncertainty and, in turn, fail to recognize when these predictions may be wrong.…

Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work…

In identification of dynamical systems, the prediction error method using a quadratic cost function provides asymptotically efficient estimates under Gaussian noise and additional mild assumptions, but in general it requires solving a…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…