Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials

TL;DR

This paper introduces a Bayesian framework for modeling thermodynamic properties of materials, improving robustness, consistency, and uncertainty quantification in predictions, demonstrated on Hafnium data.

Contribution

The paper presents a modular Bayesian approach that enhances thermodynamic models by addressing outliers, systematic errors, and providing transparent uncertainty quantification.

Findings

Framework effectively handles outliers and systematic errors.

Demonstrated accurate property modeling for Hafnium from 0 to 4900K.

Provides insights into thermodynamic assessment process.

Abstract

Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution. The goal of thermodynamic models is to capture data from both experimental and computational studies and then make reliable predictions when extrapolating to new regions of parameter space. These predictions will be impacted by artifacts present in real data sets such as outliers, systematics errors and unreliable or missing uncertainty bounds. Such issues increase the probability of the thermodynamic model producing erroneous predictions. We present a Bayesian framework for the selection, calibration and quantification of uncertainty of thermodynamic property models. The modular framework addresses numerous concerns regarding thermodynamic models including thermodynamic consistency, robustness to outliers and systematic errors by the use of hyperparameter weightings and robust Likelihood and Prior distribution choices. Furthermore, the framework's inherent transparency (e.g. our choice of probability functions and associated parameters) enables insights into the complex process of thermodynamic assessment. We introduce these concepts through examples where the true property model is known. In addition, we demonstrate the utility of the framework through the creation of a property model from a large set of experimental specific heat and enthalpy measurements of Hafnium metal from 0 to 4900K.