Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of simulated crystals. The lattice energy is a key physical property, which determines thermodynamic stability of a crystal but has no simple analytic expression. Past machine learning approaches to predict the lattice energy used slow crystal descriptors depending on manually chosen parameters. The new area of Periodic Geometry offers much faster isometry invariants that are also continuous under perturbations of atoms. Our experiments on simulated crystals confirm that a small distance between the new invariants guarantees a small difference of energies. We compare several kernel methods for invariant-based predictions of energy and achieve the mean absolute error of less than 5kJ/mole or 0.05eV/atom on a dataset of 5679 crystals.

中文翻译：

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通过晶体结构的连续等距不变量快速预测晶格能量

晶体结构预测 (CSP) 旨在通过优化原子、离子或分子的周期性排列来发现固体晶体材料。由于数百万模拟晶体的能量最小化缓慢，CSP 需要数周的超级计算机时间。晶格能是决定晶体热力学稳定性的关键物理性质，但没有简单的解析表达式。过去用于预测晶格能量的机器学习方法使用慢速晶体描述符，具体取决于手动选择的参数。周期几何的新领域提供了更快的等距不变量，这些不变量在原子扰动下也是连续的。我们在模拟晶体上的实验证实，新不变量之间的小距离保证了小的能量差异。