Machine Learning the Effective Hamiltonian in High Entropy Alloys

TL;DR

This paper introduces a machine learning approach using local atomic energies and deep neural networks to efficiently model the effective Hamiltonian in high entropy alloys, achieving high accuracy with large DFT datasets.

Contribution

It presents a novel data-driven method employing local energies and neural networks to accurately construct effective Hamiltonians for high entropy alloys.

Findings

Deep neural networks achieve high accuracy in modeling local energies.

Pair interaction models have $R^2$ scores above 0.99.

Neural networks outperform traditional models in representing effective Hamiltonians.

Abstract

The development of machine learning sheds new light on the problem of statistical thermodynamics in multicomponent alloys. However, a data-driven approach to construct the effective Hamiltonian requires sufficiently large data sets, which is expensive to calculate with conventional density functional theory (DFT). To solve this problem, we propose to use the atomic local energy as the target variable, and harness the power of the linear-scaling DFT to accelerate the data generating process. Using the large amounts of DFT data sets, various complex models are devised and applied to learn the effective Hamiltonians of a range of refractory high entropy alloys (HEAs). The testing $R^2$ scores of the effective pair interaction model are higher than 0.99, demonstrating that the pair interactions within the 6-th coordination shell provide an excellent description of the atomic local energies for all the four HEAs. This model is further improved by including nonlinear and multi-site interactions. In particular, the deep neural networks (DNNs) built directly in the local configuration space (therefore no hand-crafted features) are employed to model the effective Hamiltonian. The results demonstrate that neural networks are promising for the modeling of effective Hamiltonian due to its excellent representation power.