Neural Enhancement of the Traditional Wang–Sheeley–Arge Solar Wind Relation

Abstract The Wang–Sheeley–Arge (WSA) model has been the cornerstone of operational solar wind forecasting for nearly two decades, owing to its simplicity and physics-based formalism. However, its performance is strongly dependent on several empirical parameters that are typically fixed or tuned manually, limiting its adaptability across varying solar conditions. In this study, we present a neural enhancement to the WSA framework (referred to as WSA + ) that systematically optimizes the empirical parameters of the WSA solar wind speed relation using in situ observations within a differentiable physics-constrained pipeline. The approach operates in two stages: first, a neural optimizer adjusts WSA parameters independently for each Carrington rotation to better match the observed solar wind data. Then, a neural network learns to predict these optimized speed maps directly from magnetogram-derived features. This enables generalization of the optimization process and allows inference for new solar conditions without manual tuning. WSA + preserves the interpretability of the original relation while significantly improving the match with OMNI in situ data across multiple performance metrics, including correlation and error statistics. It consistently outperforms the traditional WSA relation across both low and high solar activity periods, with average improvements of approximately 40%. By integrating data-driven learning with physical constraints, WSA + offers a robust and adaptable enhancement, with immediate utility as a drop-in replacement in global heliospheric modeling pipelines.