  Turbulent fluctuations of the atmospheric refraction index, so-called optical
turbulence, can significantly distort propagating laser beams. Therefore,
modeling the strength of these fluctuations ($C_n^2$) is highly relevant for
the successful development and deployment of future free-space optical
communication links. In this letter, we propose a physics-informed machine
learning (ML) methodology, $\Pi$-ML, based on dimensional analysis and gradient
boosting to estimate $C_n^2$. Through a systematic feature importance analysis,
we identify the normalized variance of potential temperature as the dominating
feature for predicting $C_n^2$. For statistical robustness, we train an
ensemble of models which yields high performance on the out-of-sample data of
$R^2=0.958\pm0.001$.
