Approximation of correlation functions in phase‐field crystal model by machine learning approach

Abstract

Two different phase-field crystal (PFC) free excess energy expansions have been analyzed with respect to the order of a truncation term and to the accuracy of a pair correlation functions fitting. The coefficients of the correlation function in PFC model was found for the aluminum crystal based on the molecular dynamics data. A machine learning (ML) approach has been utilized to construct a neural network (NN) for the PFC approximation of correlation functions. The effective iteratomic potentials of the embedded atom model were used as an input data for NN training. Obtained NN predicts the coefficients of the correlation functions with the potentials data as input. Predictions were studied and verified with respect to the properties of NN and parameters of ML.

Structural phase-field crystal model for Lennard–Jones pair interaction potential

“…In cDFT the expansion of direct correlation functions with quadratic terms in reciprocal space was carried out by [38]. Such approach in fact is very close to the idea of eight-order [39] and twelve-order [40,41] fitting in PFC. Although the derivation of PFC as a consequent approximation of dynamical density functional theory with a gradient expansion involving derivatives leads to the possible instability above a certain value of the average density [26].…”