  The ionosphere is a vitally dynamic charged particle region in the Earth's
upper atmosphere, playing a crucial role in applications such as radio
communication and satellite navigation. The Slant Total Electron Contents
(STEC) is an important parameter for characterizing wave propagation,
representing the integrated electron density along the ray of radio signals
passing through the ionosphere. The accurate prediction of STEC is essential
for mitigating the ionospheric impact particularly on Global Navigation
Satellite Systems (GNSS). In this work, we propose a high-precision STEC
prediction model named DeepONet-STEC, which learns nonlinear operators to
predict the 4D temporal-spatial integrated parameter for specified ground
station - satellite ray path globally. As a demonstration, we validate the
performance of the model based on GNSS observation data for global and US-CORS
regimes under ionospheric quiet and storm conditions. The DeepONet-STEC model
results show that the three-day 72 hour prediction in quiet periods could
achieve high accuracy using observation data by the Precise Point Positioning
(PPP) with temporal resolution 30s. Under active solar magnetic storm periods,
the DeepONet-STEC also demonstrated its robustness and superiority than
traditional deep learning methods. This work presents a neural operator
regression architecture for predicting the 4D temporal-spatial ionospheric
parameter for satellite navigation system performance, which may be further
extended for various space applications and beyond.
