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 active 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. The form of the effective Hamiltonian is also revised to include some complex terms. BaTiO3, CsPbI3 and SrTiO3/PbTiO3 surface are taken as examples to show the accurateness of this approach comparing with conventional first-principles parametrization method.

翻译：基于第一性原理的有效哈密顿量被广泛用于预测和模拟铁电体及弛豫铁电体的性质。然而，有效哈密顿量的参数化方法复杂且难以处理具有复杂相互作用和/或复杂组分的系统。本文开发了一种基于贝叶斯线性回归的即时主动机器学习方法，用于参数化有效哈密顿量。参数化过程在分子动力学模拟中完成，每一步均预测能量、力和应力及其不确定性。当不确定性较大时，执行第一性原理计算以重新训练参数。该方法为任何目标系统（包括先前方法无法处理的复杂系统）提供了一种通用且自动化的有效哈密顿量参数计算方法。同时，对有效哈密顿量的形式进行了修正以纳入一些复杂项。以BaTiO₃、CsPbI₃和SrTiO₃/PbTiO₃表面为例，通过与传统的基于第一性原理的参数化方法对比，验证了本方法的准确性。