# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 6 Conclusions  
This work presents a supervised machine learning approach for forecasting encounters between heterogeneous polar satellites. The model utilizes 14-dimension synthetic input training data obtained by combining various pairs of orbital elements. The output training data are a set of 48 h time series that describe communication opportunities depending on the satellite-to-satellites distance between 1000 km and 3000 km. Directional antennas with fast pointing mechanisms are assumed. The SGP4 orbital model, which accounts for the most important perturbations in low-Earth orbits, is used to train, validate, and test the SL model based on a fully connected neural network architecture with a weighted loss function. The model performance is evaluated using two different datasets--one containing synthetic polar satellite data and another containing realistic polar satellite data from the Celestrak database. Both the distance threshold and the decision threshold necessary to convert the ground truth and the model prediction into binary signals are thoroughly examined in the Results section. The outcomes indicate that the proposed machine learning model can effectively predict realistic encounters between polar satellites with a balanced accuracy of around 90% when compared with the ground truth based on SGP4 orbit determination. This performance surpasses that of the synthetic dataset by approximately 5%. The discrepancy can be attributed to the sparse and uniformly distributed nature of synthetic satellites across the range space, leading to sporadic, distance threshold-dependent encounters and, consequently, more challenging prediction. Moreover, computational cost analysis reveals that after optimizing the trained model through parameter quantization, the time required to anticipate encounters using machine learning is six times lower compared to employing state-of-the-art methods based on orbit determination. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **TF** & **TF Lite** & **SGP4** \\ \hline Time [\(\mu\)s] & \(\approx\)60,000 & \(\approx\)70 & \(\approx\)420 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational cost obtained with GPU NVIDIA RTX A4000 with 32 GB RAM. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**T = 1500 km**} & \multicolumn{2}{c}{**T = 2000 km**} & \multicolumn{2}{c}{**T = 2500 km**} \\ \cline{2-7}  & **TestS** & **TestC** & **TestS** & **TestC** & **TestS** & **TestC** \\ \hline \(BA\)-\(BA^{\prime}\) & \(-0.3\%\) & \(0.0\%\) & \(0.5\%\) & \(0.3\%\) & \(1.1\%\) & \(0.9\%\) \\ \(F1\)–\(F1^{\prime}\) & \(1.1\%\) & \(1.0\%\) & \(1.9\%\) & \(1.2\%\) & \(1.8\%\) & \(1.5\%\) \\ \(P\)–\(P^{\prime}\) & \(4.9\%\) & \(3.1\%\) & \(3.1\%\) & \(2.1\%\) & \(1.1\%\) & \(1.1\%\) \\ \(R\)–\(R^{\prime}\) & \(-0.8\%\) & \(-0.3\%\) & \(0.9\%\) & \(0.5\%\) & \(2.1\%\) & \(1.6\%\) \\ \(AP\)–\(AP^{\prime}\) & \(2.8\%\) & \(1.8\%\) & \(2.2\%\) & \(1.4\%\) & \(1.6\%\) & \(1.1\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the previous mean performance metrics obtained with TensorFlow versus the new results with TensorFlow Lite (\(BA^{\prime}\), \(F1^{\prime}\), \(P^{\prime}\), \(R^{\prime}\), and \(AP^{\prime}\)). Conceptualization, E.F., J.A.R.-D.-A., F.B., and J.E. ; Data curation, E.F.; Formal analysis, E.F.; Funding acquisition, J.A.R.-D.-A., F.B., and J.E. ; Investigation, E.F., J.A.R.-D.-A., F.B., and J.E. ; Methodology, E.F., J.A.R.-D.-A., F.B., and J.E. ; Project administration, J.A.R.-D.-A; Resources, E.F., J.A.R.-D.-A., F.B., and J.E. ; Software, E.F.; Supervision, J.A.R.-D.-A., F.B., and J.E. ; Validation, E.F., J.A.R.-D.-A., F.B. and J.E. ; Visualization, E.F.; Writing--original draft, E.F.; Writing--review and editing, E.F., J.A.R.-D.-A., F.B., and J.E. All authors have read and agreed to the published version of the manuscript.