Structural analysis based on unsupervised learning: Search for a characteristic low-dimensional space by local structures in atomistic simulations

Abstract

Owing to the advances in computational techniques and the increase in computational power, atomistic simulations of materials can simulate large systems with higher accuracy. Complex phenomena can be observed in such state-of-the-art atomistic simulations. However, it has become increasingly difficult to understand what is actually happening and mechanisms, for example, in molecular dynamics (MD) simulations. We propose an unsupervised machine learning method to analyze the local structure around a target atom. The proposed method, which uses the two-step locality preserving projections (TS-LPP), can find a low-dimensional space wherein the distributions of datapoints for each atom or groups of atoms can be properly captured. We demonstrate that the method is effective for analyzing the MD simulations of crystalline, liquid, and amorphous states and the melt-quench process from the perspective of local structures. The proposed method is demonstrated on a silicon single-component system, a silicon-germanium binary system, and a copper single-component system.

Extraction of local structure differences in silica based on unsupervised learning

“…These descriptors, after feature selection by variance threshold and standardization, were transformed onto a low-dimensional space using the twostep locality preserving projections method (TS-LPP). 31 The TS-LPP method consists in using LPP twice, with a reduction from the LAAF dimensionality…”

“…This is why local averaging was performed. 31 For the ith atom, the locally averaged atomic fingerprint (LAAF) vector can be written as:…”

“…B.2 Two-step locality preserving projections (TS-LPP). In the two-step locality-preserving projections (TS-LPP) method, 31 the LPP transformation is applied first to obtain an intermediate space of dimension d m , then applied again on the resulting space to obtain the final low-dimensional space, using the same s value for both transformations. This method was shown to improve the results of single LPP and PCA.…”

Determination of hyper-parameters in the atomic descriptors for efficient and robust molecular dynamics simulations with machine learning forces

“…On the other hand, a linear-scaling DFT method is employed to perform MD simulations with the single z (SZ) basis sets for the SiGe and Si systems, both of which were the same systems used in ref. 51 and contain 1000 atoms. The density matrix minimization (DMM) and the extended Lagrangian Born-Oppenheimer MD methods are used for efficient and stable FPMD simulations.…”

“…The initial structures of the amorphous SiO 2 are prepared through the melt-quench process using a classical force field, while DFT simulations of the melt-quench process are employed to generate the amorphous structures of Si and SiGe systems. For the Si system, two types of amorphous structures are prepared at 300 K. 51 The structures of the liquid phase are formed by melting the crystalline phase.…”