Electric Potential Patterns Forecasting in the Southern Hemisphere with Deep Learning Techniques
Authors: Francesco Pio Ramunno, Simone Mestici, Igino Coco, Maria Walach, Stefano Massetti, Maria Federica Marcucci, Brandon Panos, André Csillaghy
Organizations: University of Applied Sciences and Arts Nortwestern Switzerland · Department of Computer Science, University of Geneva, 1211 Geneva, Switzerland · Universit´a Roma ”La Sapienza” · Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata, 605, Rome, Italy · School of Physics and Astronomy, Lancaster University, Lancaster, UK · Italian National Institute of Astrophysics - Institute for Space Astrophysics and Planetology, Via del Fosso del Cavaliere, 100, Rome, Italy
Space weather disturbances driven by the solar wind can degrade satellite navigation, disrupt radio communications, and threaten power infrastructure, making accurate forecasting of the high-latitude ionosphere's response a critical operational need. Existing approaches, empirical climatological models and physics-based magnetohydrodynamic simulations, either smooth out the ionosphere's time-dependent, non-linear response or are too computationally expensive for real-time use, while prior machine learning efforts have mostly targeted scalar indices rather than the full spatial structure of ionospheric convection. Here we train and compare three deep learning architectures, a probabilistic diffusion model conditioned on multi-variate solar wind and interplanetary magnetic field measurements at the L1 Lagrange point, an unconditioned diffusion ablation, and a deterministic U-Net baseline, to forecast Southern Hemisphere high-latitude electric potential maps derived from SuperDARN radar observations. Using five years (2020--2025) of SuperDARN data synchronised with DSCOVR L1 measurements, we evaluate the models under a single-pass regime, an extended autoregressive rollout of up to 350 frames, and an out-of-distribution case study on the intense March 2015 St.\ Patrick's Day storm, unseen during training. We find that the relative advantage of the deterministic and probabilistic approaches is not fixed: the deterministic model is competitive over short horizons and calm conditions, while the diffusion model's advantage grows and eventually dominates as the forecast horizon lengthens and the event becomes more dynamic, evidence that probabilistic, sample-based generative models are the more promising direction for operational, long-horizon space weather forecasting.
Figures & tables
Figure 1: Distribution of the total interplanetary magnetic field magnitude ∣B∣ per year, 2020–2025 (histogram, left; boxplot without outliers, right). Both the typical magnitude and its spread increase monotonically from 2020 to 2025, reflecting the ascending phase of Solar Cycle 25 covered by the training and validation data.
Figure 2: Chronological train/validation split, 2020–2025, shown against the Akasofu epsilon coupling parameter and the F10.7, sunspot number, and Dst indices (Section 3.3 ). Blue shading marks training regions, orange marks validation regions, and unshaded (white) intervals are 15-day buffer zones discarded from both splits to prevent data leakage between adjacent regions.
Figure 3: The forecasting task as a multimodal completion problem, illustrated on one real training sequence. Top: the four L1 solar wind and IMF timeseries (SWV, Bx , By , Bz ) are observed across the entire window, both past ( t−N to t0 ) and future ( t0 to tM ). Bottom: the corresponding electric potential maps are only known for the past N=15 frames (OBSERVED); the future M=7 frames (TO PREDICT, shaded) are the target of the prediction task. The bottom row shows the true, unseen ground truth for those M frames for reference.
Figure 4: Real example sequences illustrating the four evaluation regimes obtained by crossing geomagnetic activity (Akasofu ϵ ) with convection dynamism (mean frame-to-frame potential change), as defined in this section. For each regime, the most extreme validation-set example (largest ∣ϵ∣ and dynamism deviation in the direction of that regime’s label) is shown as seven evenly spaced snapshots from its input window, on a shared colour scale.
Figure 5: Single-pass versus autoregressive evaluation, illustrated on one real trajectory (gray = input frames, orange = predicted frames; window size reduced to 4 input / 3 output frames here for legibility, versus the actual N=15 / M=7 used throughout). Top : in the single-pass regime the model consumes one input window and produces one output window in a single forward pass. Bottom : in the autoregressive regime the same sliding window is applied repeatedly across the full trajectory, each row’s predicted frames becoming part of the input window for the next row, for a total of K steps.
Figure 6: Upstream drivers (IMF Bx , By , Bz ; solar wind speed; Dst index) and observed ionospheric potential map statistics (spatial mean, max − min, standard deviation, max ∣Φ∣ ) over the St. Patrick’s Day storm, 15–19 March 2015. Vertical dotted lines and shaded bands mark the three PRED_START windows used for autoregressive generation (Section 6.3 ) and their 30-minute conditioning window. The third window (17 March 06:00) falls on the main-phase onset: Bz turns sharply southward, solar wind speed jumps, Dst begins its plunge toward its storm minimum, and all four ionospheric statistics show a sharp jump immediately after the marker; the other two windows sample the pre-storm quiet interval.
Figure 7: NRMSE of the mean potential, spatial standard deviation, and Interquartile Potential Range (IPR), averaged over the full 7-frame prediction window, for each of the four activity × dynamism regimes. Here and in subsequent bar-chart figures, ↓ / ↑ next to a panel title indicate whether lower or higher values of that metric are better.
Figure 8: PS log-MSE, LPIPS, and SSIM, averaged over the full 7-frame prediction window, for each of the four activity × dynamism regimes.
Figure 9: Evolution of NRMSE(mean/std/IPR) and PS log-MSE/LPIPS/SSIM across the 7 predicted frames (14 minutes), for each of the four activity × dynamism regimes (columns). Shaded bands denote ±1 standard deviation across diffusion samples for CLASSIC/NOCOND where available.
Figure 10: CLASSIC’s advantage over U-Net, per sequence, on IPR and PS log-MSE (RMSE U-Net− RMSE CLASSIC , each computed by comparing that model’s prediction to ground truth over the 7 predicted frames of the sequence; positive favours CLASSIC), binned by decile of true per-sequence dynamism and pooled across all four activity × dynamism regimes ( n=2260 sequences: 477 each for the two high-activity regimes, 653 each for the two low-activity regimes). Bars are coloured by which model wins on average in that decile (green = U-Net, blue = CLASSIC, consistent with all other figures in this section).
Figure 11: NRMSE of the mean potential, spatial standard deviation, and IPR, averaged over the full 350-frame ( K=50 , 11h40) rollout, for each of the four activity × dynamism regimes.
Figure 12: PS log-MSE, LPIPS, and SSIM, averaged over the full 350-frame ( K=50 , 11h40) rollout, for each of the four activity × dynamism regimes.
Figure 13: Evolution of NRMSE(mean/std/IPR) and PS log-MSE/LPIPS/SSIM across the 50 AR steps (350 frames, 11h40), by activity × dynamism regime (columns). Each point averages over the 7 frames of that AR step and over the matched sequences of Figure 11 .
Figure 14: CLASSIC’s advantage over U-Net at K=50 , per sequence, on IPR and PS log-MSE (RMSE U-Net− RMSE CLASSIC , each computed over the full 350-frame rollout; positive favours CLASSIC), binned by decile of true per-sequence dynamism and pooled across all four regimes ( n=62 sequences). Same construction as Figure 10 , at K=50 instead of single-pass. Bars are coloured by which model wins on average in that decile.
Figure 15: NRMSE of the mean potential, spatial standard deviation, and IPR, averaged over the full rollout (42.0–67.4 hours) of each of the three PRED_START windows.
Figure 16: PS log-MSE, LPIPS, and SSIM, averaged over the full rollout of each of the three PRED_START windows.
Figure 17: NOCOND (no L1 conditioning) vs. ground truth, per-frame mean/max − min/std/max ∣Φ∣ , for each of the three PRED_START windows.
Figure 18: U-Net vs. ground truth, same layout as Figure 17 .
Figure 19: CLASSIC vs. ground truth, same layout as Figure 17 . Shaded bands denote ±1 standard deviation across the 3 diffusion samples.
Figure 20: Ground truth and predicted potential maps (17 March 06:00 window; CLASSIC/NOCOND sample 0) at five instants evenly spaced across the full rollout. The ground-truth max − min timeseries below marks where each instant falls (numbered dotted lines).
Figure 21: Same layout as Figure 20 , zoomed into the five most prominent local peaks of the ground-truth max − min curve during the main-phase build-up (8.5–14.6 hours after PRED_START ).
Accurately predicting fast solar wind conditions is challenging, as uncertainties are large and unquantified by traditional single-value prediction models. In particular, the risks of high-speed solar wind streams (HSSs), which can cause damage to technological infrastructure, cannot be reliably assessed without probabilistic forecasts. We present PROSWIN, a probabilistic machine learning model that forecasts the hourly solar wind speed (SWS) at Earth with a four-day lead time. The approach combines solar images and magnetograms using a deep neural network coupled to a distributional regression algorithm. Because standard error metrics underweight the relevance of HSS peaks, we further introduce the prediction score, a model-selection metric that jointly rewards timeline and HSS peak accuracy. On 14 years of data, our forecast achieves very well-calibrated uncertainties (<1% average deviation). Using the continuous ranked probability score (CRPS), a metric that assesses distributional accuracy, we obtain a timeline CRPS of 41.0 km/s, an HSS peak CRPS of 45.3 km/s, and a prediction score of 42.3 km/s. We find that the 171 Å channel is an important complement to the typically used 193 Å and 211 Å channels and that the prediction score for model selection improves the applicability of the model. Compared to selected models from the literature, ours is the only one that is accurate for both timeline and HSS peak values, rather than trading one off against the other. These results support the advantages of probabilistic over single-value solar wind models. The introduced methods are also transferable to other forecasting problems.
Daniel Collin, Yuri Shprits, Luca Chiarabini +3
Space Physics and Space Weather, GFZ Helmholtz Centre for Geosciences, Potsdam, Germany · Department of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany · Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany +5
Most data-driven ionospheric forecasting models operate on gridded products, which do not preserve the time-varying sampling structure of satellite-based sensing. We instead model the ionosphere as a dynamic graph over ionospheric pierce points (IPPs), with connectivity that evolves as satellite positions change. Because satellite trajectories are predictable, the graph topology over the forecast horizon can be constructed in advance. We exploit this property to condition forecasts on the future graph structure, which we term ephemeris conditioning. This enables prediction on lines of sight that appear only in the forecast horizon. We evaluate our framework on multi-GNSS (Global Navigation Satellite System) data from a co-located receiver pair in Singapore spanning January 2023 through April 2025. The task is to forecast Rate of TEC Index (ROTI)-defined irregularities at 5-minute cadence up to 2 hours ahead as binary probabilistic classification per node. The resulting model, IonoDGNN, achieves a Brier Skill Score (BSS) of 0.49 and a precision-recall area under the curve (PR-AUC) of 0.75, improving over persistence by 35% in BSS and 52% in PR-AUC, with larger gains at longer lead times. Ablations confirm that graph structure and ephemeris conditioning each contribute meaningfully, with conditioning proving essential for satellites that rise during the forecast horizon (receiver operating characteristic AUC: 0.95 vs.\ 0.52 without). Under simulated coverage dropout, the model retains predictive skill on affected nodes through spatial message passing from observed neighbors. These results suggest that dynamic graph forecasting on evolving lines of sight is a viable alternative to grid-based representations for ionospheric irregularity forecasting. The model and evaluation code will be released upon publication.
Accurate solar irradiance forecasting is essential for the reliable integration of photovoltaic power into modern electricity grids. All-sky imagers (ASI) provide high-resolution observations of clouds, making them well suited for intra-hour forecasting. Recent deep learning approaches have substantially improved forecast accuracy but are often limited by deterministic predictions and a reduced capability to anticipate ramp events. This work proposes FarSky, a generative forecasting framework that leverages latent-space coupling to learn task-aware representations of sky images. A multi-task autoencoder first learns a shared latent representation for image reconstruction and irradiance estimation. A latent diffusion model then generates future latent states conditioned on recent observations, from which irradiance forecasts are directly decoded. Probabilistic forecasts are inherently obtained through stochastic sampling. The framework is developed using a multi-year ASI dataset acquired at the Plataforma Solar de Almería, Spain, and evaluated on two independent test datasets against persistence, state-of-the-art end-to-end, and generative forecasting approaches. FarSky achieves the best overall deterministic and probabilistic forecasting performance, improving forecast skill by up to 11 percentage points. Furthermore, it substantially improves ramp event detection over existing methods, achieving F1-scores above 60%. These results demonstrate the potential of combining generative models with task-aware latent-space coupling for solar forecasting.
Yann Fabel, Bijan Nouri, Milon Miah +4
1DLR, Institute of Solar Research · 2RWTH Aachen University · 3CIEMAT, Energy Department, Renewable Energy Division