Uncertainty Quantification for Parameter Estimation and Response Prediction

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.