A comparison of deterministic and Bayesian inverse with application in micromechanics
Result description
The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities over parts of the boundary and Tikhonov regularization. To include uncertainties in observed values, Bayesian inversion is also considered in order to obtain a statistical description of unknown material parameters from sampling provided by the Metropolis-Hastings algorithm accelerated by using the stochastic Galerkin method. The connection between Bayesian inversion and Tikhonov regularization and advantages of each approach are also discussed.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/61989100:27240/18:10239980 RIV/61989100:27740/18:10239980
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
A comparison of deterministic and Bayesian inverse with application in micromechanics
Original language description
The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities over parts of the boundary and Tikhonov regularization. To include uncertainties in observed values, Bayesian inversion is also considered in order to obtain a statistical description of unknown material parameters from sampling provided by the Metropolis-Hastings algorithm accelerated by using the stochastic Galerkin method. The connection between Bayesian inversion and Tikhonov regularization and advantages of each approach are also discussed.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
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Volume of the periodical
63
Issue of the periodical within the volume
6
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
23
Pages from-to
665-686
UT code for WoS article
000453844300005
EID of the result in the Scopus database
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Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2018