Physics-Guided Flow Matching: A Generative AI Framework for Global Total Electron Content Forecasting

Si-Tong Yang; Feng Ye; Xian Lu; Dong Lin; Benjamin C. Martinez

cs.LGOct 27, 2026

Physics-Guided Flow Matching: A Generative AI Framework for Global Total Electron Content Forecasting

Authors: Si-Tong Yang, Feng Ye, Xian Lu, Dong Lin, Benjamin C. Martinez

Organizations: Department of Industrial Engineering, Clemson University, Clemson, SC, USA · Department of Physics and Astronomy, Clemson University, Clemson, SC, USA · Department of Physics, Utah State University, Logan, UT, USA

Abstract

Accurate forecasting of global total electron content (TEC) is important for space weather monitoring and the reliable operation of satellite communication and navigation systems. We propose a physics-guided generative artificial intelligence (AI) framework for day-ahead global TEC forecasting. The framework builds on flow matching, which learns to gradually transform samples from an initial distribution into new samples that share the statistical characteristics of the target data. The proposed model incorporates ionospheric dynamics described by a partial differential equation (PDE) into this transformation process, guiding the changes between initial and target samples using physical knowledge. The model further combines the physical dynamics with statistical patterns captured from data to learn this transformation, adaptively adjusting their relative contributions at each location. The model is trained and evaluated using one year of global TEC data generated by the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM). The results demonstrate that our model improves both spatial and temporal forecasting accuracy over representative benchmarks, including statistical, deep learning, and generative AI methods at all lead times and across latitudes. The average root mean square error (RMSE) is 39.2% lower than that of ConvLSTM and 23.8% lower than that of the same framework without physical guidance. The learned contribution weights vary systematically with latitude and across geographic locations, showing how the physical contribution changes across the forecast domain. These findings demonstrate that explicit physical guidance improves generative forecasts of global TEC and highlight the value of incorporating physical dynamics into generative AI modeling.

Figures & tables

Figure 1: Overview of ionospheric modeling frameworks, organized by modeling paradigm.

Figure 2: Overview of the dataset used in this study. (A) Global TEC field at a representative time. (B) Solar radio flux $F_{10.7}$ and (C) geomagnetic index $Kp$ over the study period. (D) Horizontal $\mathbf{E}\times\mathbf{B}$ drift field and (E) vertical $\mathbf{E}\times\mathbf{B}$ drift at the same representative time step as in (A). Colors in (D) indicate the magnitude of the horizontal drift, with arrows showing its direction, whereas colors in (E) represent the signed vertical drift velocity. Panels (A), (D), and (E) show global snapshots of the corresponding fields at 17 February 2023, 22:00 UTC.

Figure 3: Overview of the proposed model for global TEC forecasting.

Figure 4: Illustration of the difference between (A) a linear Gaussian probability path and (B) the proposed physics-guided probability path. The solid curve denotes the conditional mean path, the thin curves represent possible stochastic trajectories, and the shaded region indicates the dispersion defined by the variance schedule.

Figure 5: Comparison of TIEGCM reference TEC maps and PGFM forecasts at lead times of 1, 3, 6, and 12 hours. The forecast was initialized at 00:00 UT on 29 March 2023.

Figure 6: Latitude-resolved profiles of forecast errors and background TEC. At each

2.5^{\circ}

latitude, values were averaged over all longitudes. All profiles were smoothed using a five-point moving average for visualization. (A) RMSE, (B) MAE, and (C) nMAE. The gray dashed curves in (A) and (B) show background TEC on the right axes.

		Statistical	Deep learning	Flow matching		Diagnostic
Metric	$h$ (hour)	STGP	ConvLSTM	FMB	PGFM	Oracle a
RMSE	1	1.417	1.654	0.442	0.269	0.201
	3	3.078	2.838	1.151	0.703	0.514
	6	5.066	3.164	1.726	1.234	0.929
	12	4.829	3.054	2.562	1.869	1.642
	24	4.865	3.439	3.636	3.266	2.757

Table 1: Forecast errors at selected lead times for all evaluated models.

Figure 7: Averaged forecasting errors of different models at lead times from 1 to 24 hours: (A) RMSE, (B) MAE, and (C) nMAE.

Figure 8: Learned fusion weight $\lambda$ assigned to the physical “velocity”. Larger values indicate a greater contribution of the physical branch to the fused “velocity”. For each grid cell, $\lambda$ was first averaged over all test samples. (A) Latitudinal profiles of the resulting weights across longitude. The solid and dashed curves denote the median and mean, respectively, while the dark and light shaded regions indicate the interquartile range and the 10th–90th percentile interval. (B) Global distribution of the mean weight $\lambda$ at each grid cell. (C) and (D) Polar views of the height-integrated net $\mathrm{O}^{+}$ rate of change over the northern and southern polar regions, respectively, at 03:45 UTC on 3 September 2023. The rates are calculated by height-integrating the sum of production, loss, drift, and wind contributions and are expressed in $\mathrm{TECU\cdot h^{-1}}$ from TIEGCM outputs.

Figure 9: Predicted flow matching “velocity” maps at 03:00 UT on 29 August 2023. The panels compare the target “velocity”, the outputs of the data-driven and physical estimators, the fused PGFM prediction, and the FMB prediction. The “velocity” describes changes in the flow matching state space; positive and negative values indicate tendencies toward increasing and decreasing TEC values, respectively.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Figure 10: Architecture of the data-driven and physical“velocity”estimators. The conditional U-Net takes the intermediate TEC state

\mathrm{x}_{\tau}

, the flow coordinate

\tau

, encoded past TEC history

\mathcal{H}_{t}

and encoded physical-driver history

\mathcal{D}_{t}

as inputs to estimate the data-driven “velocity”. The ConvGRU predicts a physical basis of the “velocity” by summarizing the past ion dynamics

\mathcal{P}_{t}

and available physical drivers

\mathcal{D}_{t}

. Then the two estimates are combined at each grid cell adaptively to generate the predicted “velocity”.

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