MAGUS: Groundbreaking Crystal Structure Predictions with Machine Learning and Graph Theory
Crystal structures play a crucial role in determining the properties of various materials, making them essential in materials research. Predicting crystal structures is a method that seeks stable or metastable structures based solely on the chemical composition under specific conditions. This approach has revolutionized the discovery of new materials and exploration of different phase spaces.
However, the current crystal structure prediction techniques have faced limitations due to two significant factors. Firstly, the cost of performing structure optimization using first-principles calculations increases exponentially with the number of atoms involved. Secondly, the number of local minima on the potential energy surface also rises exponentially as the degrees of freedom increase.
To overcome these challenges, a group of researchers has proposed a novel solution that combines machine learning and graph theory. In addressing the first issue, they suggest using a machine learning potential for surrogate calculations. Initially, random structures are generated, and a subset of these structures undergoes high-level calculations to construct a training set that includes energy, force, and stress data obtained through Density Functional Theory (DFT) calculations.
This dataset is then utilized to train the machine learning potential. In subsequent searches for optimized structures, the computationally expensive DFT calculations are replaced by the machine learning force field. During this optimization process, any structures that require extrapolation are recorded.
If the extrapolation exceeds a certain threshold, DFT single-point calculations are performed on these structures, and they are added to the training set to retrain the force field and correct the potential function. This iterative process continues until the optimization can be solely carried out by the machine learning surrogate. However, calibration using first-principles calculations is still necessary to account for errors introduced by the machine learning force field.
To address the second challenge, the research team employed graph theory to reduce the search space. They utilized community detection algorithms, typically used in evolutionary algorithms, to identify excellent genes or local structural motifs. While it is challenging to determine these motifs for ordinary extended crystals, abstracting periodic crystal structures as graphs allowed for the application of community detection algorithms. For example, in the case of an extended α-boron structure, converting it into a quotient graph and subjecting it to community detection algorithms resulted in the extraction of the boron icosahedron.
By preserving this component unchanged in subsequent genetic operations, the degrees of freedom decreased significantly from 36 to 6, which substantially reduced the search space.
In testing the effectiveness of this combined approach, the research team achieved substantial progress across various fields such as planetary science, super-hard materials, high-energy density materials, and superconducting materials. The machine learning approach successfully reduced the number of self-consistent calculations by approximately two orders of magnitude. Additionally, the utilization of graph theory reduced the number of structures that needed to be explored by around 30% to reach the desired crystal structure.
In conclusion, the marriage of machine learning and graph theory has paved the way for groundbreaking advancements in crystal structure prediction. By significantly reducing computational costs and narrowing down the search space, researchers can explore a vast array of materials more efficiently and effectively. The impact of this methodology extends to various scientific fields, offering immense potential for the discovery of new materials with desirable properties.
