A High‐Precision Ionosphere Slant Total Electron Content Forecast Model Based on Physical Information Neural Network

Abstract

Ionospheric delay is a critical error source for precise positioning and timing with the BeiDou‐3 Navigation Satellite System (BDS‐3), particularly for single‐frequency users. Its rapid variability under disturbed space weather conditions poses significant challenges for short‐term forecasting. This study develops a multi‐step physics‐informed neural network (PINN) for accurate and physically consistent slant total electron content (STEC) forecasting. BDS‐3 observations are used, while reference STEC sequences are generated through spatiotemporal interpolation of Global Ionosphere Maps and thin‐shell mapping. Their consistency was validated against STEC independently derived from dual‐frequency GNSS code and carrier‐phase observations using carrier‐to‐code leveling, with correlation coefficients ranging from 0.956 to 0.991 across six stations. The proposed model integrates an 18‐dimensional feature space, including temporal variations, satellite–receiver geometry, ionospheric background conditions, and space weather parameters. A feature‐attention mechanism and residual forecasting network were employed for 5‐, 15‐, 30‐, and 60‐min forecasts. Physical constraints, including the non‐negative TEC boundary and STEC–VTEC thin‐shell mapping relationship, are incorporated into the loss function, with hyperparameters optimized through Bayesian optimization. Experimental results demonstrate that the proposed PINN outperforms the data‐only RA‐DNN and XGBoost models. Compared with the structure‐matched RA‐DNN, PINN reduces RMSE by 0.96–5.19 TECU across all station and forecast‐time combinations, demonstrating the effectiveness of incorporating physical knowledge for improved STEC forecasting.