摘要
The first-principles-based effective Hamiltonian scheme provides one of the most accurate modeling techniques 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),PbTiO_(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 107 atoms)atomic structures.
基金
the National Key R&D Programs of China(grant Nos.2022YFB3807601,2020YFA0711504)
the National Natural Science Foundation of China(grant Nos.12274201,51725203,51721001,52003117 and U1932115)
the Natural Science Foundation of Jiangsu Province(grant No.BK20200262)
S.P.and L.B.thanks the Office of Naval Research Grant No.N00014-21-1-2086
the Vannevar Bush Faculty Fellowship(VBFF)Grant No.N00014-20-1-2834 from the Department of Defense and the ARA Impact 3.0 Grant
thanks the financial support of the Luxembourg National Research Fund(FNR)through project C21/MS/15799044/FERRODYNAMICS,We are grateful to the High Performance Computing Center(HPCC)resources of Nanjing University for the calculations.
