Stratospheric airships are lighter-than-air vehicles capable of continuous flying for months. The energy balance of the airship is the key to long-duration flights. The stratospheric airship is entirely powered by the solar array. It is necessary to accurately predict the output power of the array for any flight state. Because of the uneven solar radiation received by the solar array, the traditional model based on components has a slow simulation speed. In this study, a data-driven surrogate modeling approach for prediction the output power of the solar array is proposed. The surrogate model is trained using the samples obtained from the high-accuracy simulation model. By using the input parameter preprocessor, the accuracy of the surrogate model in predicting the output power of the solar array is improved to 98.65%. In addition, the predictive speed of the surrogate model is ten million times faster than the traditional simulation model. Finally, the surrogate model is used to predict the energy balance of stratospheric airships flying throughout the year under actual global wind fields.