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.

翻译：晶体结构在从电池到太阳能电池等各个领域都不可或缺，大量研究致力于基于原子构型预测其性质。然而，现有的晶体结构预测方法主要聚焦于寻找能量函数全局最小值处的最稳定解。这种方法忽略了位于邻近局部最小值且具有不同材料特性（如导电性或抗变形性）的其他潜在有趣材料。相比之下，质量多样性算法为晶体结构预测提供了有前景的途径，其目标是寻找具有多样化特征的高性能解集合。此外，在优化晶体结构稳定性的同时兼顾其他目标（如磁性或热电效率）也可能具有重要价值。因此，本工作利用多目标质量多样性算法的能力，以寻找具有多样化特征并能实现不同目标权衡的晶体结构。我们在5种晶体体系上分析了该方法，证明其不仅能够重新发现已知的真实结构，还能找到有前景的新结构。此外，我们提出了一种目标空间可视化方法，以深入理解可能实现的目标权衡关系。