Bézier cubics’ agreement with the neural network of the TEC map

The Bézier curves submitted by Pierre Bézier in the mid-1950s are splendid differential geometric structures. The paper compares a mechanical–theoretical curve (classical-conventional) with a computer-based artificial neural network (modern). While the reader witnesses hourly TEC (TECU) modeling by the class C⁰ Bézier structure for the first time, (s)he has the opportunity to evaluate the reliable results of segmented-continuous curves with network. The Bézier structure is established by operating the differential geometrical invariants. The yielding and accuracy of the models are evaluated with the R correlation coefficient and the mean squared error. The discussion demonstrates the harmony of the two different approaches by modeling the 365-day TEC map of 2017. Then, in particular, the outputs of the intense geomagnetic storms of 28 May (Dst = − 125 nT) and 8 September (Dst = − 122 nT) are modeled and compared. Bézier curves are read segmental-continuous every 12-h TEC map in all discussions. The network, on the other hand, employs solar wind parameters to model the TEC atlas. The models obey rigorously the causality principle. The results of the discussion display that the R score reaches around 93% and 98.8% for Bézier curves and the neural network, respectively. Again, it is noticed that the mean squared error of the network model decreases to 1.1308 TECU. The curve model emerges to the reader as an alternative to neural networks in projections of space climate conditions.