Theory Seminar : Interatomic potential of iron based on machine learning
Prediction of crystal structures for alloys and compounds with arbitrary composition of elements has not been widely performed yet, while current first-principles electronic structure calculations based on density functional theories (DFT) might have enough accuracy in predicting crystal structures in most cases. One of reasons for that is due to a large computational cost to explore vast configuration space in structural prediction by using molecular dynamics and Monte Carlo simulations based on DFT. In this talk, we report an ongoing research to develop an accurate interatomic potential of iron using a neural network (NN) method being a machine learning technique as a first step towards structural prediction of magnetic intermetallic compounds. Behler et al. proposed a way of developing accurate interatomic potentials using NN by letting NN learn a series of DFT calculations . In addition to two- and three-body structural symmetry functions as structural fingerprint proposed by Behler, we further introduce four kinds of spin symmetry functions to develop interatomic potentials using NN which can treat crystal and spin structures on the same footing. The total energies of reference systems with an arbitrary spin structure, BCC, FCC, HCP, simple cubic, diamond, and their distored structures with ferro-, antiferro-, and non-magnetic, random spin structures, were carefully calculated by using a constraint scheme, which has been newly developed, based on non-collinear DFT , and all the calculated data were assembled to form a database as reference. By providing the database as a trainnig set, we trained NN with a feed-forward network structure of four layers using a back propagation, stochastic mini-batch decent, and residual minimization method. It is found that the mean difference between the reference DFT data and NN is 9.6 meV/atom, which suggests that a highly accurate interatomic potential can be developed for magnetic systems. We also discuss how the potential can be utilized to simulate crystal and spin dynamics on the same footing. J. Behler and M. Parrinello, Phys. Rev. Lett. 98, 146401.