Evaluation of Differential Equation Solutions through Traditional Techniques and Neural Networks in Quantum Simulations

The study presents a comparative analysis of algorithms of traditional numerical methods and methods using neural networks for solving ordinary differential equations. The evaluation includes both mathematical aspects and aspects of machine learning. Using the Julia programming language, neural networks and the necessary algorithms for conducting practical experiments are implemented. These experiments demonstrate outstanding achievements in the field of quantum computing. Moreover, comparing the efficiency metrics of solving differential equations using numerical methods and neural networks reveals interesting results, depending on the chosen architecture and network parameters.