About: Polynomial chaos

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Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms of a polynomial function of other random variables. The polynomials are chosen to be orthogonal with respect to the joint probability distribution of these random variables. PCE can be used, e.g., to determine the evolution of uncertainty in a dynamical system when there is probabilistic uncertainty in the system parameters. Note that despite its name, PCE has no immediate connections to chaos theory.

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rdfs:label	Polynomial chaos (en)
rdfs:comment	Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms of a polynomial function of other random variables. The polynomials are chosen to be orthogonal with respect to the joint probability distribution of these random variables. PCE can be used, e.g., to determine the evolution of uncertainty in a dynamical system when there is probabilistic uncertainty in the system parameters. Note that despite its name, PCE has no immediate connections to chaos theory. (en)
dcterms:subject	Stochastic processes
Wikipage page ID	11938767 (xsd:integer)
Wikipage revision ID	1097321846 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian inference Probabilistic Probability distribution Basis (linear algebra) Dynamical system Mechanics Functional (mathematics) Gamma function Gaussian process George Karniadakis Stochastic Kriging Proper orthogonal decomposition Student's t-distribution Surrogate model Fluid dynamics Norbert Wiener Fractional Brownian motion Prior probability Random Random variable Hermite polynomials Hilbert space Stationary increments Stochastic processes Chaos theory Karhunen–Loève theorem Orthogonal polynomials Cameron–Martin theorem Stochastic partial differential equation Sensitivity analysis Uncertainty Uncertainty quantification Variance-based sensitivity analysis Finite element method Bayesian model comparison Bayesian regression Askey-scheme Gaussian Polynomial Function Random vector Expectation value Marginalization (probability) Monte-Carlo method dbr:Wikt:basis
sameAs	Polynomial chaos Polynomial chaos Polynomial chaos Polynomial chaos
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Reflist
has abstract	Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms of a polynomial function of other random variables. The polynomials are chosen to be orthogonal with respect to the joint probability distribution of these random variables. PCE can be used, e.g., to determine the evolution of uncertainty in a dynamical system when there is probabilistic uncertainty in the system parameters. Note that despite its name, PCE has no immediate connections to chaos theory. PCE was first introduced in 1938 by Norbert Wiener using Hermite polynomials to model stochastic processes with Gaussian random variables. It was introduced to the physics and engineering community by R. Ghanem and P. D. Spanos in 1991 and generalized to other orthogonal polynomial families by D. Xiu and G. E. Karniadakis in 2002. Mathematically rigorous proofs of existence and convergence of generalized PCE were given by O. G. Ernst and coworkers in 2012. PCE has found widespread use in engineering and the applied sciences because it makes it possible to efficiently deal with probabilistic uncertainty in the parameters of a system. It is widely used in stochastic finite element analysis and as a surrogate model to facilitate uncertainty quantification analyses. (en)
prov:wasDerivedFrom	wikipedia-en:Polynomial_chaos?oldid=1097321846&ns=0
page length (characters) of wiki page	16932 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Polynomial_chaos
is Link from a Wikipage to another Wikipage of	Inverse transform sampling White noise analysis George Karniadakis Kriging PC Generalized polynomial chaos Kosambi–Karhunen–Loève theorem Sensitivity analysis Uncertainty quantification WCE List of statistics articles List of uncertainty propagation software Multifidelity simulation Wiener chaos expansion
is Wikipage redirect of	Generalized polynomial chaos Wiener chaos expansion
is Wikipage disambiguates of	PC
is foaf:primaryTopic of	wikipedia-en:Polynomial_chaos

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