Mining of effective local order parameters for classifying crystal structures: A machine learning study

Abstract

Determining local structures of molecular systems helps the scientific and technological understanding of the function of materials. Molecular simulations provide microscopic information on molecular systems, but analyzing the resulting local structures is a non-trivial task. Many kinds of order parameters have been developed for detecting such local structures. Bond-orientational order parameters are promising for classifying local structures and have been used to analyze systems with such structures as body-centered cubic, face-centered cubic, hexagonal close-packed, and liquid. A specific set of order parameters derived from Lechner’s definitional equation are widely used to classify complex local structures. However, there has been no thorough investigation of the classification capability of other Lechner parameters, despite their potential to precisely distinguish local structures. In this work, we evaluate the classification capability of 112 species of bond-orientational order parameters including Lechner’s definitions. A total of 234 248 combinations of these parameters are also evaluated. The evaluation is systematically and automatically performed using machine learning techniques. To distinguish the four types of local structures, we determine the better set of two order parameters by comparing with a conventional set. A set of three order parameters is also suggested for better accuracy. Therefore, the machine learning scheme in the present study enables the systematic, accurate, and automatic mining of effective order parameters for classifying crystal structures.

Multistep nucleation of anisotropic molecules

“…To obtain more detailed information on the static and dynamic properties of pre-transitional local structures, we constructed the free energy landscape as a function of the cluster size N and the order parameter quantifying the degree of liquid crystalline order. The order parameter Q was provided by our ML scheme 51 , 54 , and the free energy landscape was calculated by the transition probability approach based on the previous work of Mochizuki and co-workers 55 (for calculation details, refer to Methods). The latter is presented in Fig.…”

“…The time series of quenched coordinates was analyzed using the Machine Learning-aided Local Structure Analyzer (ML-LSA) 51 , 54 . Supplementary Fig.…”

Searching for local order parameters to classify water structures at triple points

“…Machine learning (ML) is promising means for automatically and systematically performing exhaustive searches. Supervised ML has searched over 1 million order parameters, and it has provided the best (set of) order parameter(s) to classify the structures of various Lennard‐Jones (LJ), 28 water, 25 liquid crystal, 29 and liquid‐crystal polymer phases 21 . The order parameters selected for a liquid crystal and its polymers are completely different from conventional orientational order parameters and exhibit much better classification accuracy 21,29 .…”

“…A total of 159,767,496 combinations of parameters are considered with the aid of supervised ML. The classification accuracy of each order parameter is automatically and systematically determined with a ML‐aided local structure analyzer (ML‐LSA) 21,28,29 . For each triple point, the best set of two order parameters was found that distinguished three structures with high accuracy.…”

“…The classification accuracy of each order parameter is automatically and systematically determined with a ML-aided local structure analyzer (ML-LSA). 21,28,29 For each triple point, the best set of two order parameters was found that distinguished three structures with high accuracy. A set of three order parameters is also suggested for better accuracy.…”