Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures

Dianjing Liu, Yixuan Tan, Erfan Khoram, and Zongfu Yu*

——||背景||——

如今，纳米光子器件大多要依赖于复杂的纳米结构来实现复杂的功能，设计难度也越来越大。传统的设计方式是建立在优化上，典型的设计是先随机设计一个结构，利用电磁模拟计算它的响应，将得到的结果与目标响应相比较，然后不断改变设计结构达到接近于目标的响应，以此迭代。传统的设计方法需要反复试错，进行多次的电磁模拟仿真，耗费大量的时间，效率低下；而且设计者需要很高的专业知识素养，才能完成设计。因此，基于机器学习的数据驱动设计方法开始涌现。

——||创新||——

在反向设计网络中，存在着反向散射的基本属性：相同的电磁属性R是由不同的结构D1，D2，…产生，这样的不唯一性使得神经网络无法收敛，极大的增加了网络的训练难度。本文提出了一个串联网络结构（tandem network structure）来解决这个问题，通过将反向设计网络与正向建模网络级联，可以有效地训练串联网络。

——||图文一览||——

图一：人工神经网络（NNs）设计模型

(a) A forward modeling neural network with one hidden layer.

(b) An inverse network with one hidden layer.

Conclusion: This is the key advantage of the data-driven method: simulations are invested in to build the design tool, while they are constantly consumed in conventional optimization methods.

图二：一个反向设计的例子

(a) A thin film composed of m layers of SiO2 and Si3N4.

(b, c) Example of two 6-layer thin film designs with very similar transmission spectra.

Conclusion: We set the maximum allowed thickness of each layer to be a. The spectral range of interest is 0.15c/a ≤ f ≤ 0.25c/a. The number of instances (R, D) typically ranges from tens to hundreds of thousands. In practice, the training data set may not include instances with identical response. However, as long as there are instances with distinct structures and almost the same transmission spectra, the training of the neural network would be hard to converge.

图三：使用全连接网络检验训练过程

(a) Learning curve of the inverse network.

(b) Test example of the inverse network trained by the unfiltered training set.

(c) Test example of the inverse network trained by the filtered training set.

Conclusion: The design produced by this NN turns out to be far off from the target spectrum. Even without apparently conflicting instances, there are still implicitly conflicting instances that cannot be easily eliminated.

图四：由连接到前向网络的反向设计网络组成的串联网络

Conclusion: The forward modeling network is trained in advance. Then, the weights in the pretrained forward modeling network are fixed and the weights in the inverse network are trained to reduce the cost function defined as the error between the predicted response and the target response.

图五：网络的训练和测试结果

(a) Learning curve of the tandem neural network.

(b, c) Example test results for the tandem network method.

Conclusion: The rapidly decreasing cost of test instances shows that training is highly effective. Indeed, the structures designed by the tandem network create the desired transmission spectra with much better fidelity.

图六：串联神经网络的设计示例

Conclusion: The spectra of the designed structures are reasonably satisfying the design goal. It only takes a fraction of a second for the neural network to compute a design.

——||结论||——

文章表明使用神经网络进行反向设计会遇到非唯一性问题，这是反向散射问题中的典型问题。这种显性或隐形的一对多的数据使得很难在大型训练数据集上训练神经网络。文章提出了一个由连接到前向网络的反向设计网络组成的串联网络，它为复杂光子结构的反向设计提供了训练大型神经网络的方法。

文献链接：ACS Photonics 2018, 5, 1365−1369

DOI: 10.1021/acsphotonics.7b01377

https://pubs.acs.org.ccindex.cn/doi/abs/10.1021/acsphotonics.7b01377

报告人：安希鹏