  High entropy alloys (HEAs) have been increasingly attractive as promising
next-generation materials due to their various excellent properties. It's
necessary to essentially characterize the degree of chemical ordering and
identify order-disorder transitions through efficient simulation and modeling
of thermodynamics. In this study, a robust data-driven framework based on
Bayesian approaches is proposed and demonstrated on the accurate and efficient
prediction of configurational energy of high entropy alloys. The proposed
effective pair interaction (EPI) model with ensemble sampling is used to map
the configuration and its corresponding energy. Given limited data calculated
by first-principles calculations, Bayesian regularized regression not only
offers an accurate and stable prediction but also effectively quantifies the
uncertainties associated with EPI parameters. Compared with the arbitrary
determination of model complexity, we further conduct a physical feature
selection to identify the truncation of coordination shells in EPI model using
Bayesian information criterion. The results achieve efficient and robust
performance in predicting the configurational energy, particularly given small
data. The developed methodology is applied to study a series of refractory
HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset
size affects the confidence we can place in statistical estimates of
configurational energy when data are sparse.
