On-the-fly machine learning for parametrization of the effective Hamiltonian

The first-principles-based effective Hamiltonian is widely used to predict and simulate the properties of ferroelectrics and relaxor ferroelectrics. However, the parametrization method of the effective Hamiltonian is complicated and hardly can resolve the systems with complex interactions and/or complex components. Here, we developed an on-the-fly machine learning approach to parametrize the effective Hamiltonian based on Bayesian linear regression. The parametrization is completed in molecular dynamics simulations, with the energy, forces and stress predicted at each step along with their uncertainties. First-principles calculations are executed when the uncertainties are large to retrain the parameters. This approach provides a universal and automatic way to compute the effective Hamiltonian parameters for any considered systems including complex systems which previous methods can not handle. BaTiO3 and Pb(Sc,Ta)O3 are taken as examples to show the accurateness of this approach comparing with conventional first-principles parametrization method.