  Recently, the machine learning force field has emerged as a powerful atomic
simulation approach for its high accuracy and low computational cost. However,
its applications in the multi-component materials are relatively less. In this
study, the ML force fields are constructed for both elemental material (Cu) and
binary material (SiO2). The atomic environments are described by the structural
fingerprint that takes the bond angle into account, and then, different ML
techniques, including linear regression, neural network and mixture model
method, are used to learn the structure-force relationship. We found that the
use of angular structural fingerprint and mixture model method significantly
improves the accuracy of ML force fields. In addition, we discussed the
effective structural fingerprints auto-selection method based on LASSO and the
genetic algorithm. The atomic simulations carried out with ML force fields are
in excellent agreement with ab initio calculations.
