AN OPTIMAL SAMPLING RULE FOR NONINTRUSIVE POLYNOMIAL CHAOS EXPANSIONS OF EXPENSIVE MODELS

2015 ◽  
Vol 5 (3) ◽  
pp. 275-295 ◽  
Author(s):  
Michael Sinsbeck ◽  
Wolfgang Nowak
Keyword(s):  
Polynomial Chaos ◽  
Optimal Sampling ◽  
Polynomial Chaos Expansions ◽  
Sampling Rule

Modeling of Stochastic EMC Problems with Anisotropic Polynomial Chaos Expansions

2021 ◽  
Vol 10 (2) ◽  
pp. 70-79
Author(s):  
Theodoros Zygiridis ◽  
Georgios Kommatas ◽  
Aristeides Papadopoulos ◽  
Nikolaos Kantartzis
Keyword(s):  
Polynomial Chaos ◽  
Polynomial Chaos Expansions

Optimal sampling for pedigree analysis: tracing a single gene

1982 ◽  
Vol 14 (4) ◽  
pp. 752-762 ◽  
Author(s):  
E. A. Thompson
Keyword(s):  
Probability Distribution ◽  
Single Gene ◽  
Pedigree Analysis ◽  
Genetic Models ◽  
Optimal Sampling ◽  
Large Pedigree ◽  
Sequential Procedures ◽  
Rare Gene ◽  
Enhance Efficiency ◽  
Sampling Rule

In fitting genetic models on the basis of observations on an interrelated structure, sequential procedures can enhance efficiency. In this paper we consider the case of a rare gene segregating in a single large pedigree. The sampling rule is dictated by the effect of observations on the genotypic probability distribution of unobserved relatives; this effect is investigated.

scholarly journals mumpce_py: A Python Implementation of the Method of Uncertainty Minimization Using Polynomial Chaos Expansions

2017 ◽  
Vol 122 ◽  
Author(s):  
David A. Sheen
Keyword(s):  
Measurement Uncertainty ◽  
First Principles ◽  
Polynomial Chaos ◽  
Software Tool ◽  
Physical Models ◽  
Physical Parameters ◽  
Experimental Measurements ◽  
Uncertainty Minimization ◽  
Polynomial Chaos Expansions ◽  
Parameter Values

The Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) was developed as a software tool to constrain physical models against experimental measurements. These models contain parameters that cannot be easily determined from first principles and so must be measured, and some which cannot even be easily measured. In such cases, the models are validated and tuned against a set of global experiments which may depend on the underlying physical parameters in a complex way. The measurement uncertainty will affect the uncertainty in the parameter values.

A Polynomial Chaos Method for Dispersive Electromagnetics

2015 ◽  
Vol 18 (5) ◽  
pp. 1234-1263 ◽  
Author(s):  
Nathan L. Gibson
Keyword(s):  
Polynomial Chaos ◽  
Fdtd Method ◽  
Debye Model ◽  
Dispersive Media ◽  
Dielectric Parameters ◽  
Polarization Model ◽  
Computational Framework ◽  
Spatial Dimensions ◽  
Yee Scheme ◽  
Polynomial Chaos Expansions

AbstractElectromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell's equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.

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