Machine Learning the Effective Hamiltonian in High Entropy Alloys with Large DFT Datasets*

The development of machine learning sheds new light on the Monte Carlo simulation of complex alloys. One major challenge, however, is that machine learning models are generally data-hungry, while the data from density functional theory (DFT) are computationally expensive. To solve this problem, we use the atomic local energy as the target variable, and harness the power of the linear-scaling DFT method to obtain large DFT data sets. This method is used to calculate the energy data of a range of MoNbTaW refractory high entropy alloys, with machine learning techniques including kernel ridge regression, Gaussian process, and artificial neural network applied to construct the effective Hamiltonian. The results demonstrate that machine learning model built on the configurational space, which naturally incorporates non-linear and multi-site interactions, can efficiently and accurately predict the DFT energy.