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

TL;DR

Problem: The WSA model's wind-speed prediction relies on tunable parameters that vary with solar conditions, limiting adaptability. Approach: WSA+ combines a per-CR neural optimizer that refits seven WSA parameters with a Swin Transformer that generalizes these mappings to new solar conditions, predicting full 2D wind-speed maps from PFSS inputs. Findings: On 129 Carrington Rotations using OMNI data, WSA+ yields substantial improvements over the baseline in 2D map fidelity and in-situ forecasts, achieving roughly a 40% gain (40% across dataset, 39% on held-out data) while preserving interpretability. Significance: The method provides a robust, physics-constrained, data-driven enhancement that can be deployed as a drop-in replacement in operational solar wind pipelines, with open-source tooling (wsaplus).

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. The developed 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 percent. 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.

Figures (7)

• Figure 1: Schematic diagram of the undertaken method to optimize and generalize the WSA solar wind speed maps. PFSS is used to derive expansion factor and minimum angular distance maps from synoptic magnetograms. These 2D maps serve as input for both neural optimizer and neural network. L-BFGS scheme is employed to generate optimized 2D WSA maps by fitting the WSA parameters to OMNI data. Swin Transformer based neural network is trained on these optimized WSA maps to learn how to produce them directly from the PFSS-derived input maps.
• Figure 2: Comparison of Carrington maps of solar wind speed at 0.1 AU for three representative CRs: CR2049, CR2080, and CR2161, at different phases of the solar cycle. Each row corresponds to a different CR, while columns show outputs from default WSA (left), per-CR optimized WSA (middle), and WSA+ (right).
• Figure 3: Comparison of solar wind speed profiles at sub-Earth latitudes for CR2065. All WSA variants are propagated from 0.1 AU to 1 AU using the HUX model. Panels (a–c) show wind speed maps along the elliptic plane, while panels (d) and (e) present the corresponding in-situ speeds at 0.1 AU and 1 AU, respectively.
• Figure 4: Comparison of model performance across 129 Carrington Rotations. Panels (a1-a4) show CR-wise variations of RMSE, MAE, DTW, and PCC for WSA and WSA+, with respect to OMNI data. Panel (b) plots the FIT score of WSA+ with sunspot number and performance tier. Panels (c1-c3) show distribution histograms of DTW, RMSE, and FIT score.
• Figure 5: Distributions of the seven empirical WSA parameters optimized for each Carrington Rotation. The points are color-coded with their Pearson correlation coefficient (PCC) with in-situ observations.