# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
## 6 Cn^2 Net Scintillometer Training with SIM Datasets: Machine Learning-Based Turbulence Profiling
The modified \(C_{n}^{2}\) profile can be further applied for generation of a new training dataset, DNN retraining and subsequent analysis of the \(C_{n}^{2}\) prediction performance using the inference ATM dataset. This process of tunable parameter modification, DNN retraining and prediction performance evaluation could be repeated to achieve better matching of DNN prediction with actual (measured with a conventional scintillometer) \(C_{n}^{2}\) data. This general approach for \(C_{n}^{2}\)-profile tuning was analyzed in several cross-dataset machine learning experiments. For initial Cn^2 Net training we used the SIM-KO-U dataset corresponding to the Kolmogorov turbulence model with \(C_{n}^{2}\) values that were independent of propagation distance (uniform). Performance of the SIM-trained Cn^2 Net was evaluated via processing of the scintillation images from the ATM#1 and ATM#2 datasets (inference datasets). The results obtained for both inference datasets are presented in Table 3 and illustrated in Figure 10 (for the ATM#2 dataset only). The measurement-vs.-prediction and prediction RMSE \(\varepsilon_{val}(c_{n}^{2})\) plots in Figure 10a,b clearly indicate that training with the initial SIM-KO-U dataset provided poor performance in \(C_{n}^{2}\) prediction. The prediction error (\(\overline{\varepsilon}_{val}\approx 0.56\)) in this case was approximately 6.4-fold higher in comparison with the corresponding error obtained when the ATM#2 dataset was utilized for both DNN training and \(C_{n}^{2}\) prediction (see Table 3). Similarly, high prediction error (\(\overline{\varepsilon}_{val}\approx 0.54\)) was observed when the SIM-KO-U-trained Cn^2 Net was used to predict \(C_{n}^{2}\) values using the ATM#1 inference dataset. Such poor Cn'2 Net performance during the inference phase can be explained by either inconsistency between the experimentally measured data and the SIM-KO-U data computed based on  
Figure 10: Results of \(C_{n}^{2}\) profiling via deep machine learning: (**a,c**) measurement-vs.-prediction plots, and (**b,d**) corresponding scatter plots characterizing standard deviation of prediction error for the Cn’2 Net models trained at the SIM-KO-uniform (U) (**a,b**) and SIM-KO-profiled (P) (**c,d**) datasets computed, respectively, for uniform (\(\kappa\ =\ 1\)) and inhomogeneous (\(\kappa\ =\ 2.5\)) refractive index structure parameter along the propagation. In both cases the measurements from the ATM#2 inference dataset were used for the \(C_{n}^{2}\) prediction (\(C_{n,0}^{2}\ =\ 1{\cdot}10^{-14}\)m\({}^{-2/3}\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DNN Training/Inference (Validation) Dataset** & \(\overline{\varepsilon}_{val}\) & \(\sigma_{\varepsilon}\) & **\# \(C_{n}^{2}\) Values** & **\# Frames** \\ \hline SIM-KO-U/ & 0.072 & 0.06 & 10,000/ & 10,000/ \\ SIM-KO-U/ & & & 10,000 & 10,000 \\ SIM-KO-U/ & 0.65 & 0.1 & 10,000 & 10,000 \\ SIM-KO-P & & & 10,000 & 10,000 \\ SIM-KO-U/ & & & 10,000/ & 10,000/ \\ ATM\#1 & 0.541 & 0.232 & 10,000/ & 10,000/ \\ SIM-KO-P/ & & & 322 & 19,336 \\ ATM\#1 & 0.130 & 0.03 & 10,000/ & 10,000/ \\ SIM-KO-U/ & & & 322 & 19,336 \\ ATM\#2 & 0.557 & 0.391 & 10,000 & 10,000 \\ ATM\#2 & & & 940 & 112,866 \\ SIM-KO-P/ & & & 10,000 & 10,000 \\ ATM\#2 & 0.140 & 0.013 & 940 & 112,866 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Averaged \(C_{n}^{2}\) prediction error \(\overline{\varepsilon}_{val}\) and its standard deviation \(\sigma_{\varepsilon}\) for Cn’2 Net models trained using simulated datasets corresponding to the Kolmogorov turbulence model with uniform (SIM-KO-U) and unevenly distributed (profiled) along the propagation path (SIM-KO-P) refractive index structure parameter. Predictions of the \(C_{n}^{2}\) values measured with a scintillometer were performed in cross-dataset machine learning experiments using scintillation images from ATM#1 and ATM#2 inference datasets collected during the atmospheric sensing trials (see Section 2).