Journal ArticleDOI
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion
Sergey Oladyshkin,Wolfgang Nowak +1 more
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TLDR
The key idea is to align the complexity level and order of analysis with the reliability and detail level of statistical information on the input parameters to avoid the necessity to assign parametric probability distributions that are not sufficiently supported by limited available data.About:
This article is published in Reliability Engineering & System Safety.The article was published on 2012-10-01. It has received 350 citations till now. The article focuses on the topics: Polynomial chaos & Probability distribution.read more
Citations
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
TL;DR: In this paper, a physics-informed deep learning with uncertainty quantification was proposed to solve the stochastic PDE problem in multi-dimensions, where multiple DNNs are designed to learn the modal functions of the arbitrary polynomial chaos (aPC) expansion of its solution.
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An introduction to sensitivity assessment of simulation models
TL;DR: A concise introductory overview of sensitivity assessment methods for simulation models, based on derivatives, algebraic analysis, sparse sampling, variance decomposition, Fourier analysis and binary classification are given.
Journal ArticleDOI
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations
TL;DR: In this article, the authors proposed the use of non-intrusive polynomial chaos expansions (PCEs) as a means to accelerate UP analysis in seawater intrusion (SWI) numerical modeling studies.
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Data-driven polynomial chaos expansion for machine learning regression
TL;DR: It is shown that a PCE metamodel purely trained on data can yield pointwise predictions whose accuracy is comparable to that of other ML regression models, such as neural networks and support vector machines.
Journal ArticleDOI
Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits
TL;DR: An overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems is provided.
References
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Journal ArticleDOI
LIII. On lines and planes of closest fit to systems of points in space
TL;DR: This paper is concerned with the construction of planes of closest fit to systems of points in space and the relationships between these planes and the planes themselves.
Book
The jackknife, the bootstrap, and other resampling plans
TL;DR: The Delta Method and the Influence Function Cross-Validation, Jackknife and Bootstrap Balanced Repeated Replication (half-sampling) Random Subsampling Nonparametric Confidence Intervals as mentioned in this paper.
Book
Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Journal ArticleDOI
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.