The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics for arbitrary unit-cell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tight-binding model. The tight-binding model encodes not only the band structure but also the symmetry properties of the Bloch waves. This allows us to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. We demonstrate that our method is also suitable to calculate strong topological invariants, even when (like the Chern number) they are not symmetry indicated. Engineering of domain walls and optimization are accelerated by orders of magnitude. Our method directly applies to any passive linear material, irrespective of the symmetry class and space group. It is general enough to be extended to active and nonlinear metamaterials.

中文翻译：

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使用深度学习快速探索拓扑带结构

周期性纳米结构的设计允许针对特定应用定制光子、声子和物质波的传输。近年来，通过工程拓扑特性，该领域得到了进一步扩展。然而，目前缺少的是快速探索和优化能带结构以及对任意晶胞几何结构的拓扑特征进行分类的有效方法。在这项工作中，我们展示了深度学习如何应对这一挑战。我们介绍了一种方法，其中神经网络首先将几何图形映射到紧束缚模型。紧束缚模型不仅对能带结构进行编码，而且对布洛赫波的对称特性进行编码。这使我们能够根据能带表示对大量几何结构进行快速分类，识别脆弱拓扑的设计。我们证明我们的方法也适用于计算强拓扑不变量，即使（如陈数）它们不对称。畴壁和优化的工程加速了数量级。我们的方法直接适用于任何被动线性材料，而与对称类和空间群无关。它足以扩展到有源和非线性超材料。