相关论文: A Comparative Study of Polynomial Chaos Expansion-…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

The paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the application of…

Sensitivity indices when the inputs of a model are not independent are estimated by local polynomial techniques. Two original estimators based on local polynomial smoothers are proposed. Both have good theoretical properties which are…

Independent sampling of orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models, using Polynomial Chaos (PC) expansions. It is known that bounding the spectral radius of a random matrix consisting…

Power system state estimation (PSSE) is commonly formulated as weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating…

This paper presents an approach for estimating Shapley effects for use as global sensitivity metrics to quantify the relative importance of uncertain model parameters. Polynomial Chaos expansion, a well established approach for developing…

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

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…

This paper extends applications of the quantum small gain and Popov methods from existing results on robust stability to performance analysis results for a class of uncertain quantum systems. This class of systems involves a nominal linear…

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial…

Computational point-of-care (POC) sensors enable rapid, low-cost, and accessible diagnostics in emergency, remote and resource-limited areas that lack access to centralized medical facilities. These systems can utilize neural network-based…

Microgrids (MGs) are regarded as effective solutions to provide ramping support to the main grid during heavy-load periods. Nevertheless, the uncertain renewable energy sources (RES) and electric vehicles (EVs) integrated into an MG may…

Sensitivity analysis (SA) and uncertainty quantification (UQ) are used to assess and improve engineering models. In this study, various methods of SA and UQ are described and applied in theoretical and practical examples for use in energy…

The growing adoption of IoT systems in industries like transportation, banking, healthcare, and smart energy has increased reliance on sensor networks. However, anomalies in sensor readings can undermine system reliability, making real-time…

The potential for cascading failure in power systems adds substantially to overall reliability risk. Monte Carlo sampling can be used with a power system model to estimate this impact, but doing so is computationally expensive. This paper…

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the…

We review the use of an external auxiliary detector for measuring the full distribution of the work performed on or extracted from a quantum system during a unitary thermodynamic process. We first illustrate two paradigmatic schemes that…

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to…