## 3 Deep Neural Networks Assisted Nanophotonics Design for Silicon Platform
### Comparision of DNNs for the Design of Nanophotonics on Silicon Platform  
In this section, we discussed some popular DNNs used as forward models and inverse models to accelerate the design process of silicon photonics. Here, we will classify and compare the advantages and disadvantages of these DNNs for the design of nanophotonics on silicon platform.  
Forward model built via DNN serves as a boosted EM simulator for devices with similar initial structures to the training data samples. A well-trained forward model can predict optical response for given geometric parameters at almost no time cost. Combining forward model with iterative optimization algorithms, geometric parameters for a target optical response can be quickly optimized. MLP and CNN are both discriminative neural networks and have been widely used for the forward models. MLP is the simplest and most efficient DNN for geometries with low DOF such as empirical structures. With increasing DOF, both the number of training data samples and the depth of MLP structure have to be increased greatly. Data dimensionality reduction approaches can also be used to map high-DOF devices to low data dimension, but tricky data preprocessing is needed in that case. Another method is to merge data preprocessing directly into DNNs like CNN, whose convolutional layers and pooling layers are innately capable of processing high-dimensional data features. CNN is widely used for components with QR-code like structure or irregular structure.  
Inverse models are more attractive for that they generate component geometry parameters for a target optical response almost without iterative optimization processes involved. However, an inverse model is much more difficult to build and train. Firstly, one optical response corresponds to not only one group of geometric parameters. Secondly, optical response usually has lower dimensionality as compared to geometry parameters. Luckily, generative neural networks such as CVAE and CGAN are capable of projecting low dimension to high dimension. Both of them try to monitor the underlying distributions of geometric parameters and optical response. The difference is that CVAE gets the underlying distribution via encoder and CGAN utilizes a discriminator to judge whether generated geometric parameters share the same distribution with data samples. This structural difference also brings training difference: CVAE trains the encoder and decoder simultaneously while CGAN trains two DNNs as generator and discriminator in an alternate way. After training, with optical response and potential variables as input, a CVAE generates device geometric parameters via a decoder while a CGAN produces geometric parameters via a generator.  
Inverse models based on unsupervised generative neural networks are also appealing because they do not require training data samples. However, the time-consuming EM simulator has to be inserted into the generative neural networks to guarantee that they obey physical laws. Once trained, unsupervised generative neural networks can also generate new geometric parameters according to target optical response without any simulator involved.