🌞 SR_SWspeed

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

📝 Published in The Astrophysical Journal Supplement Series (ApJS), 286, 58 (2026). DOI: 10.3847/1538-4365/ae985f

---

🔭 Overview

High-speed solar wind streams from coronal holes (CHs) drive recurrent geomagnetic disturbances with a periodicity of approximately 27 days. This repo applies symbolic regression (SR), via PySR, to derive a compact, interpretable formula that predicts solar wind speed at 1 AU from two EUV-derived CH parameters, the fractional CH area ($A_{CH}$) and CH contrast ($P_{CH}$), both derived from SDO/AIA 193/211 Å images, together with prior solar wind speeds. The model is trained on 2010-2024 OMNI data (January-September) and evaluated on a held-out test set (October-December each year), with ICME periods excluded.

The final formula,

$$v_t = \sqrt{A_{CH60,,t-4d} \times P_{CH30,,t-4d}} + \sqrt{v_{t-27d} \times 372}\ \text{km/s}$$

was selected from PySR's complexity/loss Pareto front as the simplest candidate that combines both $A_{CH}$ and $P_{CH}$, balancing accuracy against expression simplicity (see notebooks/05_verify_performance.ipynb's Table 1 for the full candidate list). It is compared against three baseline models, WSA-ENLIL, ESWF, and 27-day persistence, plus an average (training-set-mean) baseline, both as a continuous time series and as a high-speed-event (HSS) detection problem.

📊 Key result

Entire test period (2010–2024, October–December each year, ICME periods excluded):

Model	MAE [km/s]	RMSE [km/s]	CC	SSF_mean	SSF_27days
SR-derived formula	60.0	78.4	0.55	0.574	0.911
WSA-ENLIL	91.3	120.3	0.36	0.981	1.556
ESWF	82.3	108.9	0.38	0.722	1.145
27-day persistence	70.9	96.2	0.46	0.630	1.000
Average (training-set mean)	74.8	93.5	–	1.004	1.592

The SR-derived formula outperforms all four baseline models in MAE and RMSE, and outperforms WSA-ENLIL/ESWF/persistence in CC, across every solar cycle phase and the entire period. The average baseline beats WSA-ENLIL and ESWF in MAE/RMSE despite predicting a constant speed per phase, a reminder that pointwise error alone doesn't imply real predictive skill. SSF (Sequence Similarity Factor, Samara et al. 2022) addresses this by scoring each model's dynamic-time-warping alignment cost against OMNI, normalized against a reference (SSF_mean: the test period's own mean speed; SSF_27days: the persistence baseline, so persistence's own SSF_27days is exactly 1.000 by construction), the SR-derived formula achieves the lowest SSF under both references.

📁 Repository structure

SR_SWspeed/
├── notebooks/
│   ├── 01_convert_to_level1.5.ipynb   # AIA level 1 -> 1.5 calibration walkthrough
│   ├── 02_get_CH_parameter.ipynb      # A_CH / P_CH computation walkthrough
│   ├── 03_compare_CH_parameters.ipynb # latitude-band parameter comparison
│   ├── 04_feature_importance.ipynb    # SR input feature importance
│   ├── 05_verify_performance.ipynb    # Table 1 (formula selection) + Table 2 + Taylor diagram
│   └── 06_hss_event_detection.ipynb   # HSS/SIR event-based verification
├── src/
│   ├── data/         # FITS calibration, CH extraction, benchmark model loaders
│   ├── models/        # PySR config, corotation projection, ensemble variants
│   ├── evaluation/     # metrics (MAE/RMSE/CC/DTW/SSF), event detection & scoring
│   ├── viz/            # all figure-generation code
│   └── utils/          # ICME masking, CH preprocessing, shared helpers
└── figures/            # published figure PNGs

⚙️ Setup

conda create -n venv python=3.12
conda activate venv
pip install -r requirements.txt

🚀 Pipeline

notebooks/01–06 walk through the full methodology interactively: AIA level-1.5 calibration, $A_{CH}$/$P_{CH}$ extraction, latitude-band comparison, SR input feature importance, and the performance verification (PySR formula-selection Table 1, Table 2, Taylor diagram) and HSS event-detection results used in the paper.

📖 Citation

Seungwoo Ahn, Youngjae Kim, Mingyu Jeon, Hyun-Jin Jeong, Daeil Kim, Junmu Youn,
and Yong-Jae Moon, "A Data-driven Empirical Formula for Solar Wind Speed
Prediction Using Symbolic Regression," The Astrophysical Journal Supplement
Series, 286, 58 (2026). https://doi.org/10.3847/1538-4365/ae985f

@article{Ahn2026,
  author  = {Ahn, Seungwoo and Kim, Youngjae and Jeon, Mingyu and Jeong, Hyun-Jin and
             Kim, Daeil and Youn, Junmu and Moon, Yong-Jae},
  title   = {A Data-driven Empirical Formula for Solar Wind Speed Prediction Using Symbolic Regression},
  journal = {The Astrophysical Journal Supplement Series},
  volume  = {286},
  number  = {2},
  pages   = {58},
  year    = {2026},
  doi     = {10.3847/1538-4365/ae985f}
}