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Illuminating the property space in crystal structure prediction using Quality-Diversity algorithms

Marta Wolinska, Aron Walsh, Antoine Cully

TL;DR

This work proposes the application of Quality-Diversity algorithms to the field of crystal structure prediction through the application of Quality-Diversity algorithms to the field of crystal structure prediction.

Abstract

The identification of materials with exceptional properties is an essential objective to enable technological progress. We propose the application of \textit{Quality-Diversity} algorithms to the field of crystal structure prediction. The objective of these algorithms is to identify a diverse set of high-performing solutions, which has been successful in a range of fields such as robotics, architecture and aeronautical engineering. As these methods rely on a high number of evaluations, we employ machine-learning surrogate models to compute the interatomic potential and material properties that are used to guide optimisation. Consequently, we also show the value of using neural networks to model crystal properties and enable the identification of novel composition--structure combinations. In this work, we specifically study the application of the MAP-Elites algorithm to predict polymorphs of TiO$_2$. We rediscover the known ground state, in addition to a set of other polymorphs with distinct properties. We validate our method for C, SiO$_2$ and SiC systems, where we show that the algorithm can uncover multiple local minima with distinct electronic and mechanical properties.

Illuminating the property space in crystal structure prediction using Quality-Diversity algorithms

TL;DR

This work proposes the application of Quality-Diversity algorithms to the field of crystal structure prediction through the application of Quality-Diversity algorithms to the field of crystal structure prediction.

Abstract

The identification of materials with exceptional properties is an essential objective to enable technological progress. We propose the application of \textit{Quality-Diversity} algorithms to the field of crystal structure prediction. The objective of these algorithms is to identify a diverse set of high-performing solutions, which has been successful in a range of fields such as robotics, architecture and aeronautical engineering. As these methods rely on a high number of evaluations, we employ machine-learning surrogate models to compute the interatomic potential and material properties that are used to guide optimisation. Consequently, we also show the value of using neural networks to model crystal properties and enable the identification of novel composition--structure combinations. In this work, we specifically study the application of the MAP-Elites algorithm to predict polymorphs of TiO. We rediscover the known ground state, in addition to a set of other polymorphs with distinct properties. We validate our method for C, SiO and SiC systems, where we show that the algorithm can uncover multiple local minima with distinct electronic and mechanical properties.
Paper Structure (17 sections, 1 equation, 7 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 1 equation, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Evolutionary Algorithms
  4. Quality-Diversity
  5. MAP-Elites
  6. Computational Methods
  7. Computational Setup
  8. Fitness Function
  9. Algorithm Evaluation
  10. Results and Discussion
  11. Reference Data -- Titanium Dioxide
  12. Results -- Titanium Dioxide
  13. Identification of Reference Structures
  14. Exploration Considerations
  15. Extension to Other Systems
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Annotated MAP-Elites grid and representation of evolution in MAP-Elites solutions across generations.
  • Figure 2: Known reference structures of TiO2 with 24 atoms or fewer plotted in a MAP-Elites grid.
  • Figure 3: Median values of QD score, coverage, median fitness and maximum fitness averaged on 10 experiments across 5000 evaluations. The shaded are represents the $25^{th}$ and $75^{th}$ percentiles.
  • Figure 4: Sample archive after 5000 evaluations. Centroids where reference solutions are expected are marked with a red outline.
  • Figure 5: Visual analysis of behaviours within sample archive.
  • ...and 2 more figures