Speed and accuracy investigations of neural network algorithms for ionospheric modelling at an equatorial region

Abstract

Neural networks are very efficient tools for modeling, including ionospheric modeling. The training algorithm is important for achieving the optimum performance of the trained network. This research is therefore meant to evaluate and compare the performances of ten neural network training algorithms based on their prediction accuracies, and the duration/times taken by each of the algorithms to establish the optimum result. The neural networks were trained using electron density measurements by Radio Occultation (RO) technique from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites. Data for the period 2006 through 2021 was used. The networks were trained using about 2.9 million data points collected from the Kano region, Nigeria (5-degree rectangular region around geographic: 12.00° N, 8.59° E) after performing data quality control. The training algorithms considered in the work include: Bayesian Regularization (BR); Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFG); Conjugate Gradient with Powell/Beale (CGB); Fletcher-Reeves Conjugate Gradient (CGF); Gradient descent with momentum and adaptive learning rate (GDX); Levenberg Marquardt (LM); One Step Secant (OSS); Polak-Ribiére Conjugate Gradient (CGP); Resilient Backpropagation (RP); and Scaled Conjugate Gradient (SCG). The results showed that the BR and the LM algorithms gave the best performances in minimizing the errors of prediction (the mean RMSEs are respectively 112 and 114 $\times {10}^3$ electrons/cm³), but the RP algorithm, which came third in terms of accuracy, was significantly faster than both the LM and BR algorithms. The worst-performing algorithm in terms of accuracy was the GDX algorithm, although it was the fastest algorithm. The BFG algorithm was the worst-performing algorithm in terms of a combination of speed and accuracy. The developed neural network model was validated using ionosonde electron density measurements obtained from Ilorin, Nigeria (geographic: 8.5° N, 4.5° E; geomagnetic: 1.8° S). A comparison of the neural network, the NeQuick, and the IRI model predictions relative to the ionosonde measurements indicate that the neural network model was the best-performing model; the NN model predictions minimized the mean absolute errors (MAEs) in ∼44% of 399 ionosonde profiles investigated, the IRI model did so in ∼32%, and the NeQuick did so in ∼24%. The MAEs of the NeQuick however exhibited the best (least) variance. In overall, the NN model gave the least (best) mean of the MAEs (∼73 × 10³ cm⁻³), compared to ∼82 × 10³ cm⁻³ given by both the NeQuick and the IRI models, further supporting the idea that neural networks are excellent for present-day ionospheric modeling.