## 5 Experiment
### Experiment Setup  
Our objective is to evaluate the bit error rate (BER), as defined in Equation (6), and the time efficiency of DeepChaos+. Regarding BER, we aim to demonstrate that DeepChaos+ achieves competitive performance even with a limited amount of training data. To accomplish this, we divided the dataset \(\mathcal{X}\) into different proportions for training and testing: 20%, 40%, 60%, and 80%. For the second term, we analyze the training time and inference time of DeepChaos+ and compare it with other machine learning-based methods.  
**Hardware Configuration.** In order to run our framework efficiently, the following hardware requirements should be met. A GPU is recommended for faster training and inference, with a minimum of an NVIDIA GTX 1060 (6 GB VRAM), though more powerful options like the NVIDIA RTX 3090 or A100 are ideal for larger datasets. A minimum of 8 GB of RAM is required, but 16 GB or more is recommended for on larger datasets. Additionally, a multi-core CPU (quad-core or higher) is beneficial for data preprocessing and managing overall system performance. Our experiments is run on a system equipped with Intel Core i7 Processor, a NVIDIA GTX 4090i (24 GB VRAM) and 64 GB of RAM.  
**Comparison Methods And Metrics.** We compare DeepChaos+ with several comparison methods, including BiLSTM [61], Informer [62], GRU-D [63], and the chaos-solving module proposed within the system. For convenience, we denote the chaos-solving module in our system as TDiS. These machine learning-based methods were chosen as they represent state-of-the-art approaches in the field of time series analysis and chaos-based modeling. The comparison is based on two metrics: bit error rate and inference time (in seconds).  
**Dataset.** The dataset used in our experiment was collected by simulating the COC (chaos on carrier) and CFOC (chaos frequency on carrier) channels in a long-haul WDM (wavelength division multiplexing) optical communication system using the DP-16 QAM modulation scheme. We generated a sequence of 1,000,000 bits and passed them through the communication system. At the transmitter side, the generated sequence was combined with chaos, resulting in a chaotic-modulated signal. At the receiver side, the received signal was subjected to noise removal, resulting in a de-noised signal. It is important to note that this de-noised signal is used to evaluate the performance of the proposed TDiS (chaos-solving module) method.  
**Hyperparameter Settings.** The detailed hyperparameters used for training the model are provided in Table 1. As mentioned earlier, we employ a Knowledge Distillation technique to reduce the model size while preserving accuracy for faster inference. The student model, which is obtained through Knowledge Distillation, is partitioned into different sizes: tiny, with a total of 240,712 parameters; small, with 461,283 parameters; medium, with 920,784 parameters; and large, with 1,911,365 parameters. These variations in model size allow us to evaluate the trade-off between model complexity and performance, enabling us to select the most suitable configuration based on our specific requirements. The learning rates for the VAE (0.0003) and student (0.001) models ensure stable convergence, and the Adam optimizer is selected for its adaptive learning rate benefits. A total of 8 epochs per update and an update time step of 600 allow the model to learn effectively over time, while the mini-batch size of 128 balances speed and memory efficiency. The aggregation model uses the Informer, incorporating attention and convolution for capturing long-range dependencies, and ELU is chosen as the activation function for the VAE to prevent vanishing gradients. The VAE-student coefficient \(\lambda\) is set to 0.6 for optimal knowledge transfer, and a gradient norm of 0.5 prevents gradient explosion during training.