<p>By the scalar auxiliary variable (SAV) approach and stabilization method, the time-dependent Ginzburg-Landau equations under the zero electric potential gauge (also known as the temporal gauge) are reformulated as an equivalent physical system that still inherits the energy-decaying property. And then, for the equivalent physical system, a class of linearized and extrapolated Runge-Kutta (ERK) finite element numerical schemes are constructed, which can achieve arbitrary high-order accuracy in time. In order to demonstrate the feasibility of the numerical schemes, several specific implementation algorithms are designed. Moreover, it is rigorously proved that the proposed numerical schemes unconditionally satisfy the modified energy-decaying law in the discrete sense. Finally, the provided numerical tests verify the validity and correctness of the theoretical analysis. For comparative purposes, we additionally investigate experiments based on a neural network framework, which also demonstrate the error accuracy, and the evolution results of energy and maximum norm.</p>