# Inverse Design of Distributed Bragg Reflectors Using Deep Learning
## 3 Results and Discussion
### Tandem Model Performance  
The IDNN network was analysed by first looking at the tandem network performance, and then validating the predictions made by the IDNN. Similarly to the SNN, the tandem network training curves were evaluated for a range of model architectures. It was seen that even without the application of dropout, the validation curve converged to a lower error. This is most likely due to the presence of dropout in the SNN model; however, it was seen that low levels of dropout in the IDNN did still increase the performance further by helping model generalisation. The final mean absolute errors were 0.00770 and 0.00745 for the validation and test datasets, respectively. As expected, this is marginally higher than for the SNN, as this is both a more complex system and must incorporate the errors of both the IDNN and the SNN. The average accuracy was found to be 94.0%, with a maximum accuracy of 99.8% and a minimum accuracy of 89.52%, which appears to outperform the network presented in [16]. Breaking it down further, it was found that 68.4% of test samples were predicted with greater than 95% accuracy, and 79.5% above 90%. Figure 5 shows these accuracies presented visually. Figure 4: The predicted (blue) and anticipated (red) reflectance spectra produced by the SNN for two different structures, demonstrating its ability to predict a variety of spectral shapes. The percentage accuracies for **(a,b)** are 77% and 99%, with layer depths [21 10 50 30 60 60] and [40 50 30 10 60 50] nm, respectively. Figure 5a represents an accuracy of 90%, and shows some deviation from the target curve. However, much of the error here could be reduced though smoothing the predicted curve, as the overall shape is relatively close. Figure 5b represents a 95% accurate graph, and one can see that the predicted values match the target well, both in terms of the reflectance value and the location of the peaks and troughs along the \(x\)-axis. The latter is of more concern, as the overall shape of the spectrum has a greater effect on the perceived colour than relatively small changes in reflectance intensity. Moving to Figure 5c shows a 94% accurate plot set to represent the average accuracy. There is a small divergence between the curves at around 380-400 nm. Lastly, Figure 5d was chosen to demonstrate the model behaviour with higher reflectance value targets. This was achieved here with 97% accuracy, suggesting that the model was exposed to several instances of high reflectance. To fully evaluate the IDNN, the material parameters were extracted for a number of test samples and checked for validity. The predictions were already bounded by the sigmoid function, meaning that negative values would not occur, but unfeasibly small or large depth predictions were also checked for. Additionally, several predictions were fed back into the TMM code to check that the analytical and numerical methods were in agreement. A few such examples are given in Figure 6, and have the material depth values of [35.6 52.7 36.9 22.1 46.1 72.0] and [47.1 25.3 23.8 22.6 51.8 68.4] nm, respectively. Here, the dashed curves represent the Matlab simulated responses, and the solid curves are the tandem model predictions. Figure 5: A selection of graphs showing example plots corresponding to various levels of accuracy. These are 90%, 95%, 94%, and finally 97%, where the predicted layer depths were [83.3 56.4 89.6 46.0 66.7 3.2], [27.1 25.6 58.8 49.0 65.4 26.9], [27.4 43.8 31.2 42.5 52.9 14.8] and [69.5 63.5 61.5 38.9 17.9 21.9] nm for (**a–d**), respectively. Overall, the predictions and calculations match well, which, alongside the high spectral prediction accuracy, means that the model will perform well when designing structures within the scope of the materials present. On top of this, the model is able to make predictions in between 100 th and 10 th of a second, which is vastly faster than any other inverse design method.