Abstract

This study conducts a comprehensive analysis of artificial intelligence models' capabilities in solving advanced mathematical problems beyond Calculus II. Notably, the research focuses on evaluating the effectiveness of six optimized models, including a specially designed Physics-Informed Neural Network (PINN), in solving stochastic, linear, nonlinear, and ordinary differential equations. Our findings revealed that the optimized PINN achieved a success rate of 91.03%, outperforming most state-of-the-art artificial intelligence models. This research contributed to the development of artificial intelligence mathematical reasoning, with potential applications to high-level engineering, healthcare, research, sustainability, and big data optimization.