Uncertainty Quantification for Parameter Estimation and Response Prediction

Generalizing the Random Effects Bayesian Inferential Framework to Account for Material and Experimental Variability
  • Denielle E. Ricciardi
  • Oksana A. Chkrebtii
  • Stephen R. NiezgodaEmail author
Technical Article


Integrated Computational Materials Engineering (ICME) is an engineering approach where the materials, manufacturing process, and component designs are optimized concurrently before an actual physical component is realized. This requires the integration of models across vast length and timescales. A key benefit of ICME is the ability to reduce the bulk of expensive and lengthy experiments via tailored simulation. However, ICME introduces new challenges and limitations as the statistical confidence in the final design and manufacturing process must be established from simulation rather than experimental observation and testing. The computational materials science community has not formally adopted tools for verification and validation or UQ for materials simulations. In this study, a Bayesian hierarchical model is considered which accounts for parameter uncertainty, the inherent variability in the properties of material samples tested, and measurement noise. The Bayesian inferential framework is used to calibrate model parameters given calibration data and also to make forward predictions with a confidence level established through the highest posterior density intervals. The generality of the framework is demonstrated through two case studies: (1) parameter estimation for a crystal plasticity model which provides key microstructural and grain-level deformation information to use within the ICME chain; (2) the estimation in uncertainty in thermodynamic phase stability from multiple databases for phase stability.


Uncertainty quantification Bayesian inference Random effects Crystal plasticity VPSC CALPHAD 

Mathematics Subject Classification




Stephen R. Niezgoda and Denielle E. Ricciardi received support from The Air Force Research Laboratory under Award FA8650-17-1-5277 “Ensemble predictions of material behavior for ICMSE for additive structures”. Stephen R. Niezgoda and Oksana A. Chkrebtii received seed funding for this work through the Center for Emergent Materials: An NSF MRSEC (Chris Hammel PI, NSF Award DMR-0820414).


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Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Department of StatisticsThe Ohio State UniversityColumbusUSA
  3. 3.Department of Mechanical and Aerospace EngineeringThe Ohio State UniversityColumbusUSA

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