Machine learning (ML) methods are becoming the state-of-the-art in numerous domains, including material sciences. In this manuscript, we demonstrate how ML can be used to efficiently predict several properties in solid-state chemistry applications, in particular, to estimate the heat of formation of a given complex crystallographic phase (here, the $\sigma -$phase, $tP30$, $D{8}_b$). Based on an independent and unprecedented large first principles dataset containing about 10,000 $\sigma -$compounds with $n=14$ different elements, we used a supervised learning approach to predict all the $\sim$500,000 possible configurations. From a random set of $\sim$1000 samples, predictions are given within a mean absolute error of 23 meV at⁻¹ ($\sim$2 kJ mol⁻¹) on the heat of formation and $\sim$0.06 Å on the tetragonal cell parameters. We show that deep neural network regression results in a significant improvement in the accuracy of the predicted output compared to traditional regression techniques. We also integrated descriptors having physical nature (atomic radius, number of valence electrons), and we observe that they improve the model precision. We conclude from our numerical experiments that the learning database composed of the binary-compositions only, plays a major role in predicting the higher degree system configurations. Our results open a broad avenue to efficient high-throughput investigations of the combinatorial binary computations for multicomponent complex intermetallic phase prediction.

机器学习 (ML) 方法正在成为众多领域（包括材料科学）中的最新技术。在这份手稿中，我们展示了如何使用 ML 有效地预测固态化学应用中的几种特性，特别是估计给定复杂晶相的形成热（这里，$\sigma -$阶段， $吨磷30$, $D{8}_{乙}$）。基于一个独立且史无前例的大型第一性原理数据集，其中包含大约 10,000$\sigma -$与 $n=14$ 不同的元素，我们使用监督学习方法来预测所有 $～$500,000 种可能的配置。从一组随机$～$1000个样本，预测被23的平均绝对误差内给予 meV的 在^-1（$～$2  kJ mol ^-1 ) 的形成热和$～$ 四方晶胞参数为0.06 Å。我们表明，与传统回归技术相比，深度神经网络回归显着提高了预测输出的准确性。我们还集成了具有物理性质（原子半径、价电子数）的描述符，我们观察到它们提高了模型精度。我们从我们的数值实验中得出结论，仅由二元组合组成的学习数据库在预测更高程度的系统配置方面起着重要作用。我们的结果为多组分复杂金属间化合物相预测的组合二进制计算的高效高通量研究开辟了广阔的途径。