Robust data-driven approach for predicting the configurational energy of high entropy alloys

Abstract

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. IntroductionAs one of the typical multicomponent alloys, high entropy alloys (HEAs) consisting of four or more principal elements have been widely studied due to their exceptional mechanical properties [1,2,3,4]. The increased number of elements expand the possible combinations and potential candidates for discovering next-generation materials with enhanced properties [5,6,7]. Typically, the material properties are inherently linked to the actual state of chemical ordering, much efforts have been therefore devoted to analyze the degree of chemical ordering and to identify the order-disorder phase transitions [8,7,9,10]. Due to expensive time costs in experimental research, computational simulations, typically first-principles calculations are playing an increasingly central role in the investigation of various properties of HEAs [11,12,13].First-principles density functional theory (DFT) methods have established as a powerful and reliable tool in computational material science and have enabled critical advancements in materials properties and performance discovery [14,15]. With the increasing numerical efficiency and growing computing power (parallel and GPU computing), it is still difficult to address the challenge of DFT calculations in relatively large supercells (thousands of atoms) and intensive sampling (huge number of configurations) [16]. To characterize the orderdisorder phase transition, a straightforward way is to combine the DFT method with Monte Carlo simulations. However, this "brute-force" method is so computationally intensive that it is often i...

Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: A data-driven approach

“…Determine the EPI model parameters with Bayesian ridge regression. A model selection process is also carried out to optimize the hyper-parameters [60]. For the EPI model, this corresponds to determine the coordination shell cutoff m.…”

“…Note that due to the fixed chemical composition in canonical system, the singlesite term V p i has been absorbed into the constant, and the number of independent EPI parameters is M (M −1)/2 for a M -component system, which is the reason for the p < p requirement. The EPI model has demonstrate high accuracy to approximate the total energy in recent studies [59,60]. For fixed chemical concentrations, the pairwise iteration plays a dominant role in determining the Hamiltonian but higher-order terms may have limited impact on the EPI model.…”

“…In this work, we consider a conjugate prior for which the posterior distribution can be derived analytically and utilize the implementation in the scikit-learn package [65] for all the reported results. More hyperparameters details can be found in [60].…”

“…3. The reason to use 6 coordination shells in the model is detailed in [60], where the Bayesian information criterion (BIC) is employed to identify the best number of coordination shells. From Fig.…”

Efficient construction of linear models in materials modeling and applications to force constant expansions

“…These types of measure may serve as a useful compliment to the CV score when evaluating FC models. They were, for example, used recently to evaluate alloy cluster expansion models 46 .…”