Multi-Objective Quality-Diversity for Crystal Structure Prediction

Abstract

Crystal structures are indispensable across various domains, from batteries to solar cells, and extensive research has been dedicated to predicting their properties based on their atomic configurations. However, prevailing Crystal Structure Prediction methods focus on identifying the most stable solutions that lie at the global minimum of the energy function. This approach overlooks other potentially interesting materials that lie in neighbouring local minima and have different material properties such as conductivity or resistance to deformation. By contrast, Quality-Diversity algorithms provide a promising avenue for Crystal Structure Prediction as they aim to find a collection of high-performing solutions that have diverse characteristics. However, it may also be valuable to optimise for the stability of crystal structures alongside other objectives such as magnetism or thermoelectric efficiency. Therefore, in this work, we harness the power of Multi-Objective Quality-Diversity algorithms in order to find crystal structures which have diverse features and achieve different trade-offs of objectives. We analyse our approach on 5 crystal systems and demonstrate that it is not only able to re-discover known real-life structures, but also find promising new ones. Moreover, we propose a method for illuminating the objective space to gain an understanding of what trade-offs can be achieved.

Figures (8)

• Figure 1: Left: Illustration of crystal structure: atoms and molecules are arranged in a repeated, ordered pattern. Right: The crystal structure energy landscape is rugged with several local optima. Relaxation is a form of local optimisation that brings solutions toward local optima.
• Figure 2: The Pareto Front represents the set of different trade-offs on objectives. The hypervolume reflects the area between points on the Pareto Front and a reference point.
• Figure 3: mome -x for CSP method overview. At each iteration, solutions are selected from the grid and undergo domain-specific variation. We then perform a fixed number of relaxation steps. The new solution is evaluated via a surrogate model and added back to the archive if it belongs to the Pareto Front of the cell corresponding to its feature.
• Figure 4: Median performance of 15 seeds, the shaded regions show the inter-quartile range.
• Figure 5: Archive plot for Silicon Carbide, colour coded to show the maximum magnetism fitness in each cell. Different plots show different threshold levels for the minimum stability of solutions.