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”.

Spatiotemporal Forecasting

Spatiotemporal forecasting predicts how quantities change across locations and time, from traffic and weather to disease and environmental systems.

See all 427 papers

Aug 19, 2026

Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting

Tropical cyclones (TCs) pose severe risks from strong winds and heavy rainfall. However, forecasting their track and intensity remains challenging due to chaotic atmosphere and the rapid amplification of initial condition errors, leading to growing forecast uncertainty. While numerical weather prediction (NWP) and deep learning models have made progress, they remain computationally demanding and often fail under complex meteorological scenarios. Here, we present Tianmu-TC, a physics-constraints generative framework for global TC forecasting. Trained on Western North Pacific data, Tianmu-TC leverages physics-constraints to generate controllable outputs with reduced uncertainty thus improving forecast reliability. Experiments show Tianmu-TC outperforms deterministic and ensemble meteorological artificial intelligence models and authoritative NWP systems such as ECMWF in global ocean basins, with significantly lower computational cost. We further show Tianmu-TC performs well in challenging scenarios such as data sparsity, anomaly tracks, rapid intensification and weakening. These findings suggest physics-constraints generative AI offers a promising approach for reliable, efficient global TC forecasting.

Shiqi Zhang, Pan Mu, Cheng Huang +6

College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou & 310023, China. · School of Control Science and Engineering, Shandong University, Jinan & 250061, China. · School of Computer Science and Engineering, Tianjin University of Technology, Tianjin & 300384, China. +1

Tropical Cyclone Intensity Forecasting Weather Forecasting Physics-Informed Generative Modeling Spatiotemporal Forecasting Probabilistic Forecasting

Ask PDF

Jun 28, 2026

t-STEP: An interpretable model for Total Electron Content predictions and irregularities estimations

Earth system infrastructures relying on satellite-based technologies, such as Global Positioning System (GPS) communications, are affected by ionospheric Total Electron Content (TEC) gradients. Modeling these gradients under physical constraints remains challenging due to their dynamic and transient nature. While existing machine learning (ML) models can predict hourly TEC variations, it remains unclear whether their temporal resolution is sufficient to preserve small-scale TEC irregularities within predicted signals. To address this gap, we introduce an interpretable ML-based model, t-STEP, designed to predict TEC at a 30-second resolution and estimate irregularity signatures from the modeled signals. This high cadence enables the derivation of Rate of TEC changes (ROT) and the ROT Index (ROTI) as diagnostic indicators of ionospheric variability. The model is developed using GPS observations from solar cycle 24 at a station located at 5.49°S, 47.49°W. A multi-metric evaluation framework, including dynamic time warping, is used for robustness assessment, while SHAP (SHapley Additive exPlanations) provides insight into feature contributions. The 30-second TEC predictions achieve 91% accuracy with a mean absolute error (MAE) of 4.38 TECU during high solar activity (2015). Compared with the International Reference Ionosphere (IRI-2020), the hourly model improves accuracy by 35%, reduces absolute errors by 57%, and increases prediction skill by 54%. More importantly, the 30-second model captures TEC irregularity dynamics and morphologies during geomagnetic storms of different intensities, outperforming an attention-based Long Short-Term Memory model under the same experimental conditions. This study demonstrates the potential of a single TEC prediction framework for scalable irregularity monitoring without requiring separate models for individual transient events.

Stephen Tete, Carl Shneider, Maxime Cordy +3

Interdisciplinary Center for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City L-1855, Luxembourg · Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome 00143, Italy · Mission Space | Space Weather, Luxembourg City L-1191, Luxembourg

Time Series Forecasting Spatiotemporal Forecasting

Ask PDF

Oct 7, 2026

EC-EarthFlow: Probabilistic emulation of daily transient global climate model simulations with flow matching

We introduce EC-EarthFlow, a generative flow matching model that emulates simulations from the physical climate model EC-Earth3. The model is trained on transient simulations from EC-Earth3 (1950-2166, SSP2-4.5) to predict the day ahead temperature field from the previous days temperature as well as annual mean temperature. Predictions are made auto-regressively with rollout periods of between a month and an extended season. Using only this variable of interest, we are able to reproduce the daily variability, spatial patterns, annual cycle and long-term trend from EC-Earth3 at a substantially lower computational cost than the physical model. We demonstrate that EC-EarthFlow is stable for long inference periods, and that it can learn the physical relationships as simulated in EC-Earth3.

Kirien Whan, Nikolaj T. Mücke, Karin van der Wiel

KNMI, Utrechtseweg 297, De Bilt, 3731GA, The Netherlands · Scientific Computing, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098XG, The Netherlands · Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands +1

Climate Emulation Climate Modeling Surrogate Modeling Neural Surrogate Modeling Probabilistic Forecasting

Ask PDF

Abstract

Spatiotemporal Forecasting

Explore similar work

Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting

t-STEP: An interpretable model for Total Electron Content predictions and irregularities estimations

EC-EarthFlow: Probabilistic emulation of daily transient global climate model simulations with flow matching