Abstract: Modeling thermodynamic properties of multcomponent materials is important for both basic science and engineering applications. Unfortunately, many journal articles report thermodynamic data — especially phase equilibrium diagrams — without uncertainty or confidence intervals. In addition, the complexity of the physics and chemistry of the multicomponent materials makes evaluating the quality of the data and models quite difficult.

In this work, we discuss the theoretical, mathematical, and computational challenges associated with quantifying uncertainty in a multidimensional parametric space with application to thermodynamic data sets and equilibrium phase diagrams. The scientific approach involves a Bayesian method that simultaneously accounts for different types of data and its provenance to deliver uncertainty intervals. Data analysis is enhanced by machine learning methods.