Digital Library of Zielona Góra contains 63 052 digital objects
Object
Title: A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
Abstract:
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. ; 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. ; 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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 27, number 2 (2017) ; click here to follow the link
Language:
License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2017)
Last modified:
Jul 14, 2025
In our library since:
Jul 3, 2025
Number of object content hits:
22
All available object's versions:
https://zbc.uz.zgora.pl/publication/100608
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 27, number 1 (2017)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 27, number 2 (2017)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 27, number 3 (2017)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 27, number 4 (2017)
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| Edition name | Date |
|---|---|
| A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion | Jul 14, 2025 |
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