# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
## 7 Turbulence Models Evaluation via Machine Learning  
In the training-inference machine learning experiments discussed in Section 6 we only used the Kolmogorov power spectrum model for SIM dataset generation. Could we improve performance of the SIM-trained Cn^2 Net by utilizing a different atmospheric turbulence model for SIM dataset generation? A broader question to ask is if the machine learning framework could be applied for theoretical models assessment, evaluation of their accuracy and applicability to diverse atmospheric propagation environments? Since we already evaluated performance of the SIM-KO-trained Cn^2 Net in prediction of \(C_{n}^{2}\) values using ATM#1 and ATM#2 inference datasets, and since, as discussed in Section 5, \(C_{n}^{2}\) measurements do not always reflect in-situ changes in atmospheric turbulence dynamics, it would be rational to compare different power spectrum models in cross-dataset training-inference machine learning experiments using the SIM-KO-trained Cn^2 Net as a reference. In the analysis presented in this section, both training and inference datasets were generated using the split-step operator technique described in Section 3. Turbulence-induced refractive index random fluctuations were represented by sets of statistically homogeneous, isotropic thin phase screens obeying one of the following well-known power spectrum models (see Appendix A): [PERSON] (1951), [PERSON], [PERSON] and [PERSON] (1959); [PERSON] (1959). The corresponding SIM datasets are referred to as SIM-KO, SIM-TA, SIM-VK and SIM-AN. The refractive index structure parameter \(C_{n}^{2}\) was assumed to be constant along the propagation path (uniform \(C_{n}^{2}\) profile). The Kolmogorov SIM-KO dataset was used for Cn^2 Net training, and the other datasets for inference. Note that the inner \(l_{0}\) and outer \(L_{0}\) scale parameters for the [PERSON] and [PERSON] power spectrum models (see Appendix A) were equal to the numerical grid pixel size (\(l_{0}\)= 1 mm) and overall grid dimension (\(L_{0}=1.0\) m), respectively. Figure 11: Examples of selected intensity scintillation images from SIM-KO-U (**top row**), SIM-KO-P and ATM#2 (**bottom row**) datasets corresponding to different turbulence strength as indicated by \(C_{n}^{2}\) values above each column. We also considered two additional inference datasets generated for the so-called non-Kolmogorov power spectrum model (SIM-NK datasets). The results of the Cn'2 Net cross-dataset training-inference experiments with different inference SIM datasets are presented in Table 4 and illustrated in Figure 12. In all cases the datasets were composed of 15,000 computer simulated scintillation images corresponding to the cosine-type \(C_{n}^{2}(m)\) dependence described by Equation (1) and shown in Figure 12 as the ground truth curve. DNN performance was evaluated using prediction errors \(\overline{\varepsilon}_{\text{val}}\) averaged across the entire \(C_{n}^{2}\) range and their standard deviations \(\sigma_{\varepsilon}\). To evaluate the DNN ability to distinguish between scintillation images generated using different power spectrum models, compare the prediction errors presented in Table 4 obtained in the cross-dataset training-inference experiments with the corresponding value \(\overline{\varepsilon}_{\text{val}}=0.072\) computed in training-validation simulations when non-overlapping subsets of the SIM-KO dataset were used for both Cn'2 Net training and \(C_{n}^{2}\) prediction (validation). The observed relatively small (\(<\)3%) difference in the prediction errors and their standard deviations suggests that scintillation images corresponding to the Kolmogorov, Tatarskii, Von Karman and Andrews turbulence models have nearly identical (undistinguished by the Cn'2 Net) spatial features, and from this viewpoint are alike.