Active learning of effective Hamiltonian for super-large-scale atomic structures

TL;DR

This paper introduces an active machine learning method using Bayesian linear regression to efficiently parameterize effective Hamiltonians for large-scale atomic structures, enabling accurate simulations of complex ferroelectric materials.

Contribution

It proposes a universal, automatic approach for parameterizing effective Hamiltonians with active learning, suitable for super-large-scale atomic systems.

Findings

Accurately models ferroelectric materials like BaTiO3 and Pb(Zr,Ti)O3.

Reduces need for extensive first-principles calculations.

Demonstrates applicability to systems with over 10^7 atoms.

Abstract

The first-principles-based effective Hamiltonian scheme provides one of the most accurate modeling technique for large-scale structures, especially for ferroelectrics. However, the parameterization of the effective Hamiltonian is complicated and can be difficult for some complex systems such as high-entropy perovskites. Here, we propose a general form of effective Hamiltonian and develop an active machine learning approach to parameterize the effective Hamiltonian based on Bayesian linear regression. The parameterization is employed in molecular dynamics simulations with the prediction of energy, forces, stress and their uncertainties at each step, which decides whether first-principles calculations are executed to retrain the parameters. Structures of BaTiO$_3$, Pb(Zr$_{0.75}$Ti$_{0.25}$)O$_3$ and (Pb,Sr)TiO$_3$ system are taken as examples to show the accuracy of this approach, as compared with conventional parametrization method and experiments. This machine learning approach provides a universal and automatic way to compute the effective Hamiltonian parameters for any considered complex systems with super-large-scale (more than $10^7$ atoms) atomic structures.