Dual adaptive sampling and machine learning interatomic potentials for modeling materials with chemical bond hierarchy

The development of reliable and flexible machine learning based interatomic potentials (ML-IPs) is becoming increasingly important in studying the physical properties of complex condensed matter systems. Besides the structure descriptor model for total energy decomposition, the trial-and-error approach used in the design of the training dataset makes the ML-IP hardly improvable and reliable for modeling materials with chemical bond hierarchy. In this work, a dual adaptive sampling (DAS) method with an on the fly ambiguity threshold was developed to automatically generate an effective training dataset covering a wide temperature range or a wide spectrum of thermodynamic conditions. The DAS method consists of an inner loop for exploring the local configuration space and an outer loop for covering a wide temperature range. We validated the developed DAS method by simulating thermal transport of complex materials. The simulation results show that even with a substantially small dataset, our approach not only accurately reproduces the energies and forces but also predicts reliably effective high-order force constants to at least fourth order. The lattice thermal conductivity and its temperature dependence were evaluated using the Green-Kubo simulations with ML-IP for $\mathrm{Co}{\mathrm{Sb}}_{3}$ with up to third-order phonon scattering, and those for ${\mathrm{Mg}}_{3}{\mathrm{Sb}}_{2}$ with up to fourth-order phonon scattering, and all show good agreements with experiments. Our work provides an avenue to effectively construct a training dataset for ML-IP of complex materials with chemical bond hierarchy.