A comparison of deterministic and Bayesian inverse with application in micromechanics

Radim Blaheta; Michal Béreš; Simona Domesová; Pengzhi Pan

Applications of Mathematics (2018)

  • Volume: 63, Issue: 6, page 665-686
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Blaheta, Radim, et al. "A comparison of deterministic and Bayesian inverse with application in micromechanics." Applications of Mathematics 63.6 (2018): 665-686. <http://eudml.org/doc/294428>.

@article{Blaheta2018,
abstract = {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.},
author = {Blaheta, Radim, Béreš, Michal, Domesová, Simona, Pan, Pengzhi},
journal = {Applications of Mathematics},
keywords = {inverse problems; Bayesian approach; stochastic Galerkin method},
language = {eng},
number = {6},
pages = {665-686},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A comparison of deterministic and Bayesian inverse with application in micromechanics},
url = {http://eudml.org/doc/294428},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Blaheta, Radim
AU - Béreš, Michal
AU - Domesová, Simona
AU - Pan, Pengzhi
TI - A comparison of deterministic and Bayesian inverse with application in micromechanics
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 6
SP - 665
EP - 686
AB - 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.
LA - eng
KW - inverse problems; Bayesian approach; stochastic Galerkin method
UR - http://eudml.org/doc/294428
ER -

References

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