Applications of Mathematics

, Volume 63, Issue 6, pp 665–686 | Cite as

A comparison of deterministic and Bayesian inverse with application in micromechanics

  • Radim BlahetaEmail author
  • Michal Béreš
  • Simona Domesová
  • Pengzhi Pan


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.


inverse problems Bayesian approach stochastic Galerkin method 

MSC 2010

86-08 82-08 65N21 65C60 60-08 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  • Radim Blaheta
    • 1
    Email author
  • Michal Béreš
    • 2
    • 3
    • 4
  • Simona Domesová
    • 2
    • 3
    • 4
  • Pengzhi Pan
    • 5
  1. 1.Institute of Geonics of the CASOstravaCzech Republic
  2. 2.Institute of Geonics of the CASOstravaCzech Republic
  3. 3.Department of Applied Mathematics, Faculty of Electrical Engineering and Computer ScienceVŠB – Technical University of OstravaOstravaCzech Republic
  4. 4.IT4Innovations National Supercomputing CenterVŠB – Technical University of OstravaOstravaCzech Republic
  5. 5.Institute of Rock and Soil MechanicsChinese Academy of Sciences, XiaohongshanWuchang, WuhanChina

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