PMGC-SimVP: Parametric Multi-scale Gated Convolution for Global Ionospheric TEC Prediction

Conference: ECCV 2026
Paper: ECCV Official
Area: Time Series
Keywords: Ionospheric TEC Prediction, Space Weather, Parameter Conditioning, Spatiotemporal Prediction, Multi-scale Gated Convolution

TL;DR

To tackle severe non-stationarity and pronounced latitudinal heterogeneity in global ionospheric Total Electron Content (TEC) under space weather disturbances, this paper proposes PMGC-SimVP, a purely convolutional framework featuring a two-stage low-rank temporal adapter, latitudinally structured parameter modulation, and dual-baseline residual learning, slashing parameters by over 90% while significantly boosting storm-time forecasting accuracy and long-horizon stability.

Background & Motivation

The spatiotemporal variability of global ionospheric Total Electron Content (TEC) governs radio wave propagation delays, playing an indispensable role in Global Navigation Satellite System (GNSS) positioning accuracy, satellite communication reliability, and real-time space weather early warning. However, the ionosphere is a highly dynamic plasma system continuously driven by solar radiation and geomagnetic disturbances. Under extreme space weather events such as solar flares and geomagnetic storms, ionospheric TEC undergoes violent non-stationary evolutions. Traditional empirical and semi-empirical models, including Klobuchar, IRI, and NeQuick, rely on compact parameterizations and simplified physical assumptions, failing to produce high-fidelity global grid forecasts under disturbed geomagnetic regimes. While deep spatiotemporal predictors (such as ConvLSTM, PredRNN, and SimVP) have shown promise in short-term forecasting, standard computer vision architectures typically treat consecutive frames as an isolated autonomous system, making them fundamentally vulnerable to abrupt dynamical regime shifts induced by external physical forcing.

Directly transferring generic vision predictors to global ionospheric forecasting exposes three fundamental bottlenecks. First, solar activity and geomagnetic storms induce strong non-stationarity, causing pure history-based extrapolation models to suffer severe performance degradation during disturbance events. Second, the global geomagnetic configuration and solar illumination angle impose extreme latitudinal heterogeneity: the Equatorial Ionization Anomaly (EIA) crests and high-latitude auroral zones exhibit completely divergent responses under identical space weather drivers. Existing concatenation-based conditioning or spatially uniform modulations ignore this spatial heterogeneity, while standard rectangular latitude-longitude grids introduce boundary discontinuities and geometric distortions. Third, as the forecast horizon extends to 24 hours, recursive and autoregressive predictors inevitably suffer from error accumulation and spatial over-smoothing, undermining operational forecast stability.

To overcome these challenges, this paper formulates global TEC forecasting as a conditional spatiotemporal prediction problem, recognizing the necessity of decoupling the globally stable background structure from parameter-sensitive local dynamics while endowing external physical drivers with spatial awareness. Core idea: built upon a purely convolutional SimVP backbone, PMGC-SimVP compresses high-dimensional sequence complexity via a two-stage low-rank temporal adapter, injects external space weather drivers into a parallel Slow-Fast convolution network through latitudinally structured gated modulation and dynamic prototype kernel adaptation, and stabilizes long-horizon extrapolation via dual-baseline residual learning.

Method

Overall Architecture

PMGC-SimVP adopts an encoder-adapter-translator-decoder architecture to forecast future 24-hour global TEC maps (\(T_{\mathrm{out}}=24\)) from historical 48-hour observations (\(T_{\mathrm{in}}=48\)) and time-varying space weather external driver sequences \(\mathcal{P}_{\mathrm{in}}\).

The spatial encoder extracts per-frame 2D feature representations and applies Earth-aware padding (circular padding along longitude and replicate padding along latitude) to eliminate spherical boundary artifacts. A two-stage low-rank temporal adapter then decouples temporal reduction from cross-channel mixing, compressing the temporal features into a compact latent representation. Concurrently, the Parametric Context Encoding (PCE) module uses multi-query attention pooling to distill a global context vector from time-varying solar and geomagnetic parameters (such as F10.7, SSN, Dst, Ap, and X-ray flux). The latent features then pass through a translator composed of stacked PMGC Blocks, where a Slow branch models global topological structures while a Fast branch handles multi-scale local dynamics conditioned on latitudinal band modulation and dynamic kernels. Finally, the spatial decoder predicts non-stationary residuals, which are added onto a deterministic dual-baseline combining short-term inertia and diurnal periodicity.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    InState["Historical 48h TEC Maps + Space Weather Drivers"] --> Adapt["Two-Stage Low-Rank Temporal Adapter<br/>Grouped temporal compression + pointwise projection"]
    Adapt --> SlowFast["Slow-Fast Parallel PMGC Architecture<br/>Global axial convolution + local multi-scale convolution"]
    SlowFast --> Mod["Latitudinally Structured Gated Modulation & Dynamic Kernels<br/>Band-wise FiLM modulation + prototype kernel adaptation"]
    Mod --> Res["Dual-Baseline Residual Learning & Masked Loss<br/>Inertial/diurnal dual baseline + masked Charbonnier"]
    Res --> Out["Future 24h Global TEC Forecast Maps"]

Key Designs

1. Two-Stage Low-Rank Temporal Adapter: Decoupling Temporal Compression from Channel Mixing

Standard SimVP models flatten temporal features and process them with dense projections. When the input history reaches 48 frames, the quadratic complexity \(O(T_{\mathrm{in}} \cdot C_{\mathrm{hid}}^2)\) causes parameters and memory consumption to explode. To eliminate this bottleneck, the temporal adapter separates temporal compression from cross-channel mixing into two low-rank stages. First, a grouped 1D temporal convolution with group count \(g=C_{\mathrm{hid}}\) independently compresses the temporal length from \(T_{\mathrm{in}}\) to a compact temporal rank \(r_t\) within each channel. Second, a pointwise convolution mixes cross-channel representations and projects them to a channel rank \(r_c\).

This design drastically reduces computational complexity to \(O(C_{\mathrm{hid}} \cdot T_{\mathrm{in}} \cdot r_t + C_{\mathrm{hid}} \cdot r_t \cdot r_c)\). With \(T_{\mathrm{in}}=48\), \(r_t=12\), and \(r_c=64\), it slashes temporal module parameters and FLOPs by over 95%. As a result, the entire PMGC-SimVP model requires only 9.89M parameters (merely 5.07% of SimVP's 195M) and achieves a remarkable inference throughput of 1745.2 FPS.

2. Slow-Fast Parallel PMGC Architecture: Decoupling Global Structure from Multi-Scale Local Dynamics

Global ionospheric evolution involves both smooth, large-scale background diurnal cycles and fine-grained, localized violent turbulence (such as EIA crest bifurcation and polar patch formations). Blending them into isotropic convolutions risks corrupting global structural integrity with local high-frequency noise. The PMGC Block decouples these processes into a parallel Slow-Fast structure. The Slow branch captures global spatial structure using large-kernel axial depthwise convolutions:

\[\mathbf{Z}_{\mathrm{slow}} = \mathrm{DWConv}_W\big(\mathrm{DWConv}_H(\mathbf{Z})\big)\]

The Fast branch models fine-grained local dynamics using multi-scale depthwise convolutions across multiple kernel sizes, guided by a lightweight routing network \(\mathcal{R}(\tilde{\mathbf{Z}})\) that predicts spatially adaptive path weights \(\alpha_k\):

\[\mathbf{Z}_{\mathrm{fast}} = \sum_{k=1}^{K_S} \alpha_k \odot \big(\mathbf{W}_k \tilde{\mathbf{Z}}\big), \quad \alpha = \mathcal{R}(\tilde{\mathbf{Z}})\]

The branch outputs and input representations are adaptively fused via Grouped Spatial Softmax Fusion (GSSF), followed by a lightweight gMLP and two residual updates to refine the spatiotemporal features.

3. Latitudinally Structured Gated Modulation & Dynamic Kernels: Spatially Aware Physical Conditioning

External drivers exert highly non-uniform physical impacts across latitudes: low latitudes are governed by equatorial fountain effects producing sharp EIA gradients, while high latitudes are dominated by particle precipitation and magnetospheric convection. Naive channel-wise concatenation cannot capture such spatial heterogeneity. PMGC addresses this through a dual mechanism of band-wise feature modulation and dynamic prototype kernel adaptation.

At the feature level, the PCE module summarizes exogenous drivers into a global context vector \(\mathbf{v}_{\mathrm{ctx}}\). Conditioned on learnable latitudinal band embeddings \(\mathbf{e}_M\), the model generates \(M\) band tokens \(\mathbf{R}_M = \phi(\mathrm{Norm}(\mathbf{v}_{\mathrm{ctx}} \mathbf{e}_M))\), which are broadcast along latitude rows and multiplied with spatial content gates \(\mathbf{A}\) to compute pixel-wise FiLM scaling and shifting modulators \(\gamma\) and \(\beta\):

\[\mathbf{Z}_{\mathrm{mod}} = \mathbf{Z} \odot \gamma + \beta\]

At the weight level, PMGC maintains a shared prototype kernel dictionary \(\mathcal{K} = \{K_d\}_{d=1}^D\) with \(K_d \in \mathbb{R}^{3 \times 3}\). Using a unified global context \(\mathbf{u}_{\mathrm{global}}\) that aggregates band representations and spatial attention pooling, the network dynamically predicts path-specific coefficients \(a_{b,k,d}\) to assemble custom convolution kernels on the fly:

\[\mathbf{W}_{k,c} = \mathbf{W}_{k,c} + \sum_{d=1}^D a_{b,k,d} K_d\]

This ensures that external space weather intensity and regional latitudinal identity directly modulate the directional filtering and frequency selectivity of local convolutional operations.

4. Dual-Baseline Residual Learning & Masked Loss: Anchoring Long Horizons and Suppressing Grid Artifacts

In long-horizon autoregression, deep models frequently suffer from error accumulation and mean drift. To guarantee forecast stability, the framework decomposes future states into a deterministic prior and a learnable non-stationary residual:

\[\hat{\mathcal{X}}^{(t)} = \mathcal{X}_{\mathrm{base}}^{(t)} + \Delta \mathcal{X}^{(t)}\]

The deterministic baseline \(\mathcal{X}_{\mathrm{base}}^{(t)}\) smoothly transitions from short-term physical inertia to long-term diurnal periodicity:

\[\mathcal{X}_{\mathrm{base}}^{(t)} = \alpha_t \cdot X_{\mathrm{last}} + (1 - \alpha_t) \cdot X_{\mathrm{diurnal}}^{(t)}\]

where \(X_{\mathrm{last}}\) is the last observed TEC map and \(X_{\mathrm{diurnal}}^{(t)}\) is the diurnal reference at the target hour. The weight \(\alpha_t\) linearly decays from 1 to 0 across the forecast horizon, smoothly anchoring the long-term trend while allowing the network to dedicate its capacity to learning non-stationary residuals \(\Delta \mathcal{X}^{(t)}\).

Loss & Training

The model is trained end-to-end using a masked Charbonnier loss. Due to the spherical topology of the Earth, coordinate transformation introduces geometric distortions near polar regions. A fixed binary validity mask \(\Omega_{\mathrm{valid}}\) excludes padded polar rows, calculating the robust reconstruction loss strictly over physically valid grid cells (\(71 \times 72\)):

\[\mathcal{L} = \frac{1}{T_{\mathrm{out}} \cdot |\Omega_{\mathrm{valid}}|} \sum_{t=1}^{T_{\mathrm{out}}} \sum_{(h,w) \in \Omega_{\mathrm{valid}}} \sqrt{\big(\hat{\mathcal{X}}_t(h,w) - \mathcal{X}_t(h,w)\big)^2 + \epsilon^2}\]

with smoothing parameter \(\epsilon = 10^{-3}\). All models are optimized using AdamW (learning rate \(5 \times 10^{-4}\), batch size 16) on a single NVIDIA RTX 4090D GPU.

Key Experimental Results

Main Results

Quantitative evaluations comparing PMGC-SimVP against leading spatiotemporal forecasting methods on the 2023 storm-time test set (ascending phase of Solar Cycle 25 with frequent severe geomagnetic storms) and across overall test periods are summarized below. PMGC-SimVP achieves superior performance across all metrics, with performance advantages widening significantly under stormy conditions.

Method	2023 Stormy MAE ↓	2023 Stormy RMSE ↓	2023 Stormy SSIM ↑	Overall Average MAE ↓	Overall Average RMSE ↓	Overall Average SSIM ↑
SimVP [8]	3.257	4.815	0.933	2.043	3.515	0.959
PredRNN-v2 [37]	3.568	5.196	0.922	2.256	3.809	0.952
TAU [30]	3.359	4.826	0.930	2.119	3.532	0.957
WaST [22]	2.986	4.439	0.940	1.882	3.248	0.964
Stormer [21]	3.133	4.581	0.933	1.978	3.357	0.959
Met2Net [16]	3.028	4.500	0.941	1.896	3.288	0.964
PMGC-SimVP (Ours)	2.801	4.159	0.946	1.774	3.051	0.967

Regional temporal consistency (Pearson correlation coefficient, Corr.) and spatial gradient fidelity (isotropic gradient RMSE, Grad.) across latitudinal zones under 2023 stormy conditions:

Method	Low Lat. Corr. ↑	Low Lat. Grad. ↓	Mid Lat. Corr. ↑	Mid Lat. Grad. ↓	High Lat. Corr. ↑	High Lat. Grad. ↓
SimVP [8]	0.971	1.037	0.963	0.622	0.909	0.468
PredRNN-v2 [37]	0.965	1.224	0.955	0.729	0.896	0.523
TAU [30]	0.970	1.025	0.959	0.642	0.908	0.486
WaST [22]	0.975	0.969	0.968	0.577	0.921	0.443
Stormer [21]	0.973	1.206	0.965	0.723	0.919	0.553
Met2Net [16]	0.975	0.961	0.967	0.582	0.917	0.451
PMGC-SimVP (Ours)	0.978	0.914	0.971	0.553	0.930	0.428

Ablation Study

Ablation experiments evaluate the contribution of individual architectural components and parameter conditioning modes across latitude zones and overall metrics:

Config	Low Lat. MAE ↓	Mid Lat. MAE ↓	High Lat. MAE ↓	Overall MAE ↓	Overall RMSE ↓	Note
Ours (Full Model)	2.426	1.453	1.471	1.774	3.051	Full parallel Slow-Fast with parameter modulation
w/o Dual-Baseline Residual	2.530	1.503	1.528	1.844	3.161	Without dual baseline prior; error accumulation worsens
w/o Charbonnier	2.497	1.530	1.536	1.845	3.164	Replaced with standard L1/L2 reconstruction loss
w/o PMSC	2.455	1.481	1.516	1.808	3.132	Without multi-scale local dynamic convolution
w/o Param Condition	2.462	1.480	1.500	1.804	3.118	Without space weather driver conditioning
w/o SA	2.455	1.475	1.505	1.802	3.092	Without axial large-kernel spatial aggregation slow branch
Ours (Param=0)	-	-	-	1.823	3.074	Model weights fixed; parameter inputs zeroed out
Ours (Param-Shuffled)	-	-	-	1.784	3.066	Model weights fixed; parameter inputs shuffled in batch

Key Findings

• Crucial synergy of dual baseline and parameter conditioning: Removing the dual-baseline residual increases overall RMSE from 3.051 to 3.161, with low-latitude MAE degrading by 0.104, confirming its role in preventing long-sequence error drift. Removing parameter conditioning raises RMSE to 3.118, demonstrating that external space weather inputs supply vital non-stationary regime-shift cues.
• Physical attribution reveals dynamic regime shifts: Gradient-based input attribution reveals that during Calm periods (Dst \(> -30\text{ nT}\)), model predictions are dominated by background radiative descriptors (C-class flares, F10.7, X-ray flux). Under Intense Storms (Dst \(\le -100\text{ nT}\)), the attribution score of the magnetospheric ring current index Dst surges dramatically, reflecting the true physical transition to magnetosphere-ionosphere electrodynamic coupling.
• High efficiency and low footprint: On an RTX 4090D GPU, PMGC-SimVP requires only 9.89M parameters and 19.91 GFLOPs—slashing model size compared to SimVP (195M / 91.71 GFLOPs) and WaST (142M / 175 GFLOPs). It achieves 1745.2 FPS inference throughput with 5.97 GB memory consumption.
• Cross-task generalization: Evaluated without exogenous parameters on standard spatiotemporal benchmarks (WeatherBench and TaxiBJ), the pure PMGC convolutional backbone surpasses ConvLSTM, PredRNN, SimVP, and WaST (reaching 1.026 MSE on WeatherBench and 28.3 MSE on TaxiBJ), demonstrating strong general-purpose spatiotemporal modeling capability.

Highlights & Insights

• Spatially structured parameter modulation: Instead of crudely concatenating 1D scalar drivers with 2D spatial feature channels, PMGC employs latitudinal band tokens and dynamic kernel generation, allowing external space weather conditions to selectively adapt local filtering responses according to latitude-dependent physical regimes.
• Decaying dual-baseline strategy: The seamless linear transition from last-frame physical inertia to historical diurnal periodicity provides a reliable prior anchor, simultaneously maintaining short-term continuity and bounding long-term error drift without complex autoregressive training.
• Decoupled low-rank temporal modeling: By splitting temporal modeling into grouped 1D temporal convolutions and pointwise channel projections, the framework resolves the longstanding parameter and memory explosion in SimVP-style sequence modeling.

Limitations & Future Work

• Late-stage performance degradation in extreme superstorms: In the case study of the April 23–24, 2023 severe superstorm (minimum Dst of -213 nT), the model's advantage diminishes beyond \(T \ge 67\text{ h}\). This occurs because prolonged storm-time negative phases produce deep, persistent electron depletions, whereas the model's dual baseline gradually reverts toward normal diurnal climatology.
• Coarse driver parameterization: The model currently utilizes macroscopic planetary indices (such as Dst, Ap, and F10.7). Incorporating high-cadence upstream solar wind measurements (\(B_z\), solar wind dynamic pressure) and auroral electrojet indices (\(AE\)) represents a promising avenue for finer-grained nowcasting.
• Resolution scaling: The current validation operates on a global \(71 \times 73\) grid. Extending the framework to high-resolution regional TEC grids and multi-source data assimilation remains future work.

Related Work & Insights

• vs SimVP [8]: SimVP relies on unconstrained dense temporal projections (195M parameters) and lacks external conditioning mechanisms. PMGC-SimVP reduces parameters to 9.89M via low-rank temporal adapters while introducing latitudinally conditioned modulation and dual-baseline residual learning.
• vs WaST [22]: WaST leverages wavelet transforms for multi-scale frequency modeling but incurs heavy compute overhead (142M parameters, 175 GFLOPs) and lacks physical driver conditioning. PMGC-SimVP achieves a 5x speedup and lowers storm-period RMSE from 4.439 to 4.159.
• vs Visual Conditioning Methods (FiLM [23] / CondConv [39]): Generic conditional modulation methods are designed for planar isotropic vision tasks. PMGC tailors conditional modeling to planetary-scale geophysical fields by introducing Earth-aware boundary padding, latitudinal band tokens, and regime-dependent dynamic kernel adaptation.

Rating

• Novelty: ⭐⭐⭐⭐☆ Elegantly tailored architecture addressing ionospheric non-stationarity and latitudinal heterogeneity via low-rank temporal compression and band-wise modulation.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive evaluation covering storm-period benchmarks, latitudinal decomposition, 24-hour horizon stability, physical parameter attribution, and generic video generalization.
• Writing Quality: ⭐⭐⭐⭐⭐ Rigorous methodology, crisp motivation, well-organized technical descriptions, and self-consistent tables and formulas.
• Value: ⭐⭐⭐⭐☆ Highly valuable for operational GNSS error mitigation and space weather hazard forecasting; serves as a lightweight, efficient template for conditional geophysical forecasting.