Uncertainty quantification and propagation in CALPHAD modeling

Design is about making decisions bounded by a quantifiable degree of certainty. In the context of alloy design, Integrated Computational Materials Engineering (ICME) provides the framework whereby performance requirements are ultimately transformed into alloy/processing specifications through the combination of (complex) computational models connecting process-structure-property-performance relationships and experiments. Most ICME approaches consider the models used as deterministic and thus do not provide the means to make alloy design decisions with proper confidence measures. At the root of ICME lie CALPHAD models that describe the thermodynamics and phase stability of phases under specific thermodynamic boundary conditions. To date, the vast majority of efforts within the CALPHAD community have been deterministic in that thermodynamic models and the resulting thermodynamic properties and phase diagram features do not explicitly account for the uncertainties inherent in the model formulation or in the experimental/computational data used. In this contribution, we provide an overview of the state of the field. We review major efforts thus far and we then provide a (brief) tutorial on basic concepts of uncertainty quantification and propagation (UQ/UP) in CALPHAD. We discuss the major features of frequentist and Bayesian interpretations of uncertainty and proceed with a discussion of recent case studies in which UQ has been used to parameterize models for the thermodynamic properties of phases. We follow our discussion by presenting frameworks and demonstrating the propagation of uncertainty in thermodynamic properties and phase diagram predictions and briefly discuss how we can use Bayesian frameworks for rigorous model selection as well as for model fusion. We close our contribution by providing context for what has been done and what remains to be accomplished in order to fully embrace the management of uncertainty in CALPHAD modeling, a foundational element of ICME.