This study explores the use of neural network methods and analytical modifications of classical numerical methods to solve dynamic engineering problems. We focus on constructing parametric models of physical and engineering objects using neural networks based on physical principles. The experimental setup involves the nonlinear bending of a hollow cantilever beam under distributed and concentrated forces. Results are evaluated based on accuracy, labor intensity, and model stability. Neural network models, particularly those with fewer basis functions, and models based on modifications of numerical methods, provided the most accurate solutions. However, neural network methods required more computation time and were less stable compared to numerical methods, which offered faster and more reliable results. These findings highlight the potential of combining neural network approaches with classical numerical methods for improved accuracy and efficiency in engineering applications.