The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method, supported by machine learning techniques, that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution, we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice, and could be generalized to interacting systems.

中文翻译：

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统计和机器学习方法指导的工程拓扑阶段

寻找具有拓扑特性的材料是一项持续的工作。在本文中，我们提出了一种受机器学习技术支持的系统统计方法，该方法无需事先了解相图即可构建通用格的拓扑模型。通过从随机分布中采样紧密绑定参数向量，我们获得了用相应的拓扑索引标记的数据集。然后分析该标记的数据，以提取与拓扑分类最相关的那些参数，并找到它们最可能的值。我们发现参数的边际分布已经定义了拓扑模型。参数之间的关联中隐藏了其他信息。