The “one-to-many” problem is a typical challenge that faced by many machine learning aided inverse nanophotonics designs where one target optical response can be achieved by many solutions (designs). Although novel training approaches, such as tandem network, and network architecture, such as the mixture density model, have been proposed, the critical problem of solution degeneracy still exists where some possible solutions or solution spaces are discarded or unreachable during the network training process. Here, we report a solution to the “one-to-many” problem by employing a conditional generative adversarial network (cGAN) that enables generating sets of multiple solution groups to a design problem. Using the inverse design of a transmissive Fabry–Pérot-cavity-based color filter as an example, our model demonstrates the capability of generating an average number of 3.58 solution groups for each color. These multiple solutions allow the selection of the best design for each color which results in a record high accuracy with an average index color difference ΔE of 0.44. The capability of identifying multiple solution groups can benefit the design manufacturing to allow more viable designs for fabrication. The capability of our cGAN is verified experimentally by inversely designing the RGB color filters. We envisage this cGAN-based design methodology can be applied to other nanophotonic structures or physical science domains where the identification of multi-solution across a vast parameter space is required.

中文翻译：

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结构颜色的逆向设计：通过条件生成对抗网络找到多种解决方案

“一对多”问题是许多机器学习辅助的逆纳米光子学设计面临的典型挑战，其中一个目标光学响应可以通过多种解决方案（设计）来实现。尽管已经提出了诸如串联网络等新颖的训练方法和混合密度模型等网络架构，但在网络训练过程中一些可能的解决方案或解决方案空间被丢弃或无法到达的情况下，解决方案退化的关键问题仍然存在。在这里，我们通过使用条件生成对抗网络（cGAN）报告了“一对多”问题的解决方案，该网络能够为设计问题生成多个解决方案组的集合。以透射式法布里-珀罗腔彩色滤光片的逆向设计为例，我们的模型展示了为每种颜色生成平均 3.58 个解决方案组的能力。这些多种解决方案允许为每种颜色选择最佳设计，从而实现创纪录的高精度，平均指数色差 Δ乙0.44。识别多个解决方案组的能力可以使设计制造受益，从而允许制造更可行的设计。我们的 cGAN 的能力通过反向设计 RGB 滤色器进行了实验验证。我们设想这种基于 cGAN 的设计方法可以应用于其他纳米光子结构或物理科学领域，其中需要在巨大的参数空间中识别多解决方案。