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		<identifier>oai:zbc.uz.zgora.pl:85657</identifier>
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<dc:title xml:lang="pl"><![CDATA[A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion]]></dc:title>
<dc:creator><![CDATA[Tagade, Piyush M.]]></dc:creator>
<dc:creator><![CDATA[Choi, Han-Lim]]></dc:creator>
<dc:subject xml:lang="pl"><![CDATA[Bayesian framework]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[stochastic partial differential equation]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[Karhunen-Loéve expansion]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[generalized polynomial chaos]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[dynamically biorthogonal field equations]]></dc:subject>
<dc:description xml:lang="pl"><![CDATA[This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loéve expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.]]></dc:description>
<dc:publisher><![CDATA[Zielona Góra: Uniwersytet Zielonogórski]]></dc:publisher>
<dc:contributor><![CDATA[Korbicz, Józef (1951- ) - red.]]></dc:contributor>
<dc:contributor><![CDATA[Uciński, Dariusz - red.]]></dc:contributor>
<dc:date><![CDATA[2017]]></dc:date>
<dc:type xml:lang="pl"><![CDATA[artykuł]]></dc:type>
<dc:identifier><![CDATA[http://www.zbc.uz.zgora.pl/repozytorium/Content/85657/AMCS_2017_27_2_1.pdf]]></dc:identifier>
<dc:identifier><![CDATA[https://zbc.uz.zgora.pl/repozytorium/dlibra/publication/100608/edition/85657/content]]></dc:identifier>
<dc:identifier><![CDATA[oai:zbc.uz.zgora.pl:85657]]></dc:identifier>
<dc:source xml:lang="pl"><![CDATA[AMCS, volume 27, number 2 (2017)]]></dc:source>
<dc:source xml:lang="pl"><![CDATA[https://www.amcs.uz.zgora.pl/?action=papers&issue=104]]></dc:source>
<dc:language><![CDATA[eng]]></dc:language>
<dc:relation><![CDATA[oai:zbc.uz.zgora.pl:publication:100608]]></dc:relation>
<dc:rights xml:lang="pl"><![CDATA[Biblioteka Uniwersytetu Zielonogórskiego]]></dc:rights>
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