# Optimizing Generative Adversarial Network (GAN) Models for Non-Pneumatic Tire Design
## 2 Test Methods
### StyleGAN v2-ADA  
StyleGAN v2-ADA is an adaptive discriminator augmentation mechanism for solving the problem of overfitting with less data [45]. To train for modern high-resolution high-quality images, \(10^{5}\) to \(10^{6}\) images are required. If overfitting occurs with fewer training images, the feedback from the discriminator becomes meaningless, and the learning results begin to diverge. To solve this problem, data augmentation is used during deep learning to prevent overfitting. For example, rotating an image or applying noise to it to train an image classifier increases the invariance of the image to semantic-preserving distortions and increases the performance of the image classifier. These image variations can be used to make the images generated by full GAN more realistic and diverse. However, augmentation leakage can occur where the distribution of the augmented images follows the distribution of the original dataset, producing images with different characteristics. To avoid the above problems, StyleGAN v2-ADA proposes four solutions.  
Stochastic discriminator augmentation: StyleGAN v2-ADA is a model with an architecture similar to that of bCR [46]. However, in the StyleGAN v2-ADA architecture, we removed the CR loss term from bCR and modified the model so that the discriminator uses only the images with augmentation applied. The generator also learns using only the images with augmentation applied. We call this approach stochastic discriminator augmentation.  
Design augmentations that do not leak: If the data are augmented or corrupted to allow an invertible transformation, the discriminator can find the distribution of normal images from the corrupted images [47]. This can be achieved by making the images with normal distributions non-leaking with an appropriate fraction (\(p<1\)) of the augmented images.  
Adaptive discriminator augmentation: ADA is a method of dynamically automating the control based on the degree of overfitting to reduce the effort and time for learning by manually adjusting the hyperparameters. The basic method of measuring overfitting is using a separate validation set and observing the difference from the training set. This  
Figure 7: Image generation results of StarGAN v2.  
method has the disadvantage of having to split the validation set even if small amounts of training data are available. However, using Equation (7), ADA can quantify overfitting without a validation set.  
\[\mathrm{r}_{\mathrm{v}}=\frac{\mathbb{E}[\mathrm{D}_{\mathrm{train}}]-\mathbb{E }[\mathrm{D}_{\mathrm{validation}}]}{\mathbb{E}[\mathrm{D}_{\mathrm{train}}]- \mathbb{E}[\mathrm{D}_{\mathrm{generated}}]}\ \ \ \mathrm{r}_{\mathrm{t}}=\mathbb{E}[\mathrm{sign}( \mathrm{D}_{\mathrm{train}})] \tag{7}\]  
Our enhancement pipeline: Given the diversity of images, we have organized our pipeline into 18 transformation types, which can be grouped into six categories: pixel blitting (x-flips, 90\({}^{\circ}\) rotations, and integer translations), general geometric transformations, color transformations, image-space filtering, additive noise, and cropping. We applied the transformations in a fixed order. The strength of the augmentation was controlled by a scalar \(p\). We found that as long as \(p\) is kept below a safety threshold, the generator produces only clean images.  
Figure 8 is the result of training for 2000 epochs using the Training New Networks command of StyleGAN v2-ADA with the hyperparameters set to default. When trained with StyleGAN v2-ADA, the image quality is significantly improved compared to that of the original GAN and DCGAN, and the pattern shape is relatively diverse. However, the circles were squashed, the tire shape was not properly visible, and the shape was not consistently generated. We used the FID calculation code built into StyleGAN v2-ADA and obtained an FID of 42.88 and an LPIPS of 0.3806.