# Polynomial Modeling of Noise Figure in Erbium-Doped Fiber Amplifiers
## 4 Results and Discussion
### Full Dataset Models  
The same models are then created using the entire datasets for training, rather than a random 70% of their entries. The test set is composed of the average of all datasets for each device. This approach aims to identify errors specific to the model functions, such as the polynomial fits, and to evaluate whether a polynomial fit is appropriate for this model or if there is potential for improvement in the regression function.  
The models created are the same as in the previous case in terms of brand, gain range, and number of datasets. The results are shown in Figure 15. For absolute errors, the 90%-threshold varies between 0.05 and 0.11 dB, depending on the model, while the 99%-threshold ranges from 0.09 to 0.23 dB. In terms of relative errors, the 90%-threshold spans from 1.01 to 1.74%, while the 99%-threshold falls within 1.79 to 3.27%, depending on the model. The highest observed absolute and relative errors are 0.42 dB and 7.06%, respectively, both recorded for Juniper devices operating in the low-gain range. Notably, despite being trained on a single dataset, the EDFA-17 exhibits higher relative errors than the EDFA-35 in the low-gain range. The error contribution from the model is approximately on par with the measurement uncertainties within the dataset, as illustrated in Figure 13. This indicates that the polynomial form used for the fitting function introduces an error level  
Figure 14: Cumulative distribution of absolute and relative errors of 70–30 split models. (**a**) Absolute errors; (**b**) Absolute errors, detail; (**c**) Relative errors; (**d**) Relative errors, detail. In (**b,d**) green and red dashed lines represent 99% and 90%-threshold values, respectively, with green and red bullets highlighting minimum and maximum values obtained through these curves.  
comparable to the inherent measurement uncertainty. Therefore, modeling the noise figure as a polynomial function of the four input parameters is a valid and effective approach.  
The results obtained for the prediction of the noise figure are comparable to those achieved using machine-learning approaches for EDFA noise figure prediction. Specifically, from the literature we can observe that an Artificial Neural Network (ANN) approach yields a Mean Absolute Error (MAE) of 0.1 dB [36], while a deep neural network (DNN) approach achieves a MAE of 0.2 dB [37]. Both approaches, however, exhibit the common limitations of machine-learning techniques, such as the need for large datasets (4000 points and 45,000 points, respectively) and long training times (5000 epochs for each model). Additionally, the results are also comparable to those obtained using a Gradient Boosting Regression (GBR) approach, which produces an MAE of 0.3428 dB [31]. These comparisons highlight the effectiveness of the proposed method in providing competitive noise figure predictions while addressing typical challenges faced by machine-learning models.  
Figure 15: Cumulative distribution of absolute and relative errors of full dataset models. (**a**) Absolute errors; (**b**) Absolute errors, detail; (**c**) Relative errors; (**d**) Relative errors, detail. In (**b**,**d**) green and red dashed lines represent 99% and 90%-threshold values, respectively, with green and red bullets highlighting minimum and maximum values obtained through these curves.