Leveraging Deep Learning-based Foundation Models for Optical Turbulence ($C_n^2$) Estimation under Data Scarcity

Data-driven estimation of optical turbulence ($C_n^2$) remains challenging because high-quality training data are sparse and expensive to obtain. This study examines whether tabular foundation models (TFMs) can mitigate this limitation through pretraining on large and diverse collections of tabular datasets that are unrelated to optical turbulence. Using meteorological and turbulence observations from the Mauna Loa Observatory, we evaluate two state-of-the-art TFMs (TabPFNv2 and TabDPT) in a few-shot learning setting without any task-specific fine-tuning or hyperparameter optimization. Both models capture the observed diurnal evolution and full dynamic range of $C_n^2$, with TabPFNv2 providing superior data efficiency and ensemble stability. Their performance matches or surpasses that of previously reported data-driven and physics-based approaches applied to the same dataset. Feature importance analysis further shows that TabPFNv2 has learned physically meaningful relationships, with strong emphasis on potential temperature gradient and diurnal variability consistent with surface layer theory. These findings demonstrate the promise of TFMs as fast, tuning-free, plug-and-play tools for operational optical turbulence prediction in data-limited environments.