A Data-driven Empirical Formula for Solar Wind Speed Prediction Using Symbolic Regression

In this study, we apply symbolic regression (SR) to solar wind speed data at 1 au to derive a data-driven formula as a function of coronal hole (CH) parameters. We use two CH parameters, the fractional CH area ( A CH ) and the CH contrast ( P CH ), derived from the Solar Dynamics Observatory/Atmospheric Imaging Assembly 193 and 211 Å images as input data, together with prior solar wind speeds. We train the SR model using data spanning from 2010 May to 2024 December, with the dataset divided into a training set (January–September) and a test set (October–December) to account for the solar cycle effect. Using the PySR Python package, we derive interpretable formulae for the solar wind speed and select the optimal formula via cross validation. The SR model derives a new data-driven formula given by A C H × P C H + v t − 27 d × 372 , achieving a root-mean-squared error of 78.4 km s −1 and a correlation coefficient of 0.55. This formula shows better performance than conventional empirical models, suggesting that it captures key relationships between the CH parameters and solar wind speed. The first term indicates the acceleration component governed by CHs, and the second term indicates the background component given by the geometric mean of the 27 day persistence speed and the typical slow solar wind speed. These results suggest that SR provides a physically interpretable and explicit relationship between CH parameters and solar wind speed.