Multi-Parameter Prediction of Solar Wind Based on Deep Learning

When interacting with the Earth’s magnetosphere, high-speed plasma flows in the solar wind can trigger space weather events such as geomagnetic storms. Therefore, accurately forecasting solar wind parameters is critical for early warnings of space weather and the stable operation of modern technological systems. This study employs TimeXer, a deep learning model incorporating patch embedding and cross-attention mechanism, to explore the complex dependencies among solar wind speed, dynamic pressure, proton density, and proton temperature. This model can accurately predict solar wind parameters for the next 72 hours by only using historical solar wind data and time information, and it is also interpretable. Test results during low solar activity level (Year 2021) and high solar activity level (Year 2024) periods demonstrate the following conclusions. TimeXer’s Root Mean Square Errors (RMSE) for solar wind speed, dynamic pressure, proton density, and proton temperature are 68.39 km·s^–1, 2.12 nPa, 5.02 cm^–3, and 8.83×10⁴ K, respectively, while the Mean Absolute Errors (MAE) are 47.65 km·s^–1, 1.00 nPa, 3.13 cm^–3, and 4.49×10⁴ K. Compared with traditional and advanced deep learning methods, TimeXer exhibits superior performance, and even can accurately capture the overall variation trends of solar wind parameters during geomagnetic storm. Optimal prediction performance is achieved with a historical input length of 336 hours (corresponding to approximate 14-day quasi-period of the solar wind). The joint modeling prediction based on the inter-parameter dependencies of solar wind parameters is significantly better than the single-parameter prediction. Cross-attention weight analysis reveals that the four solar wind parameters contribute similarly to proton temperature and solar wind speed predictions. The solar wind speed and proton temperature contribute more to the prediction of proton density, while the proton temperature, solar wind speed, and annual time information have a more substantial influence on the prediction of solar wind dynamic pressure. Moreover, the importance of time information grows with increasing scales of time information.