<p>This study introduces a method based on a gradient neural network (GNN), a type of artificial neural network (ANN), for solving time-varying matrix inversion problems. Detailed step-by-step algorithms are provided along with a convergence theorem to guide the selection of optimal learning parameters. The momentum acceleration method has been integrated into the iterative process to improve the convergence rate. Additionally, the optimal value of the momentum parameter has been calculated to further enhance the algorithm’s performance. The proposed methods are demonstrated to be efficient and reliable through a series of numerical examples, which also include performance comparisons with existing algorithms. Furthermore, the practical utility of these methods is explored, specifically in image encryption and decryption based on matrix inversion and in solving the one-dimensional second-order wave equation.</p>