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

{\Pi}-ML: A dimensional analysis-based machine learning parameterization of optical turbulence in the atmospheric surface layer