Artificial Intelligence Techniques for Solving Differential Equations: A Comprehensive Re view

Differential equations are fundamental to modeling physical, biological, and engineering systems. Traditional numerical methods such as finite difference, finite element, and Runge-Kuttamethods have been widely used to solve differential equations but often suffer from computational complexity and scalability limitations. Recently, Artificial Intelligence (AI), particularlymachine learning and deep learning techniques, has emerged as a powerful alternative for solvingdifferential equations. This review paper presents a comprehensive overview of AI-based methods for solving ordinary and partial differential equations, including Physics-Informed NeuralNetworks (PINNs), Deep Neural Networks (DNNs), Gaussian Processes, and hybrid approaches.The paper discusses their methodologies, advantages, challenges, and applications across various domains. Results indicate that AI-based approaches provide flexibility, mesh-free solutions,and improved generalization capabilities. However, issues such as training instability, datarequirements, and interpretability remain significant challenges. The paper concludes with future research directions focusing on hybrid models, scalability, and integration with traditionalnumerical methods.