<p>Differential equations serve as a foundational tool for the quantitative analysis and prediction of natural phenomena and engineering systems. However, obtaining exact solutions is often intractable due to nonlinearities, high dimensionality, and complex boundary conditions. Moreover, traditional numerical methods face limitations in scalability and efficiency, particularly for large-scale or nonlinear problems. To address these challenges, artificial intelligence (AI)-based approaches have emerged as promising alternatives. This study provides a comprehensive overview of three major categories of AI techniques for solving differential equations. The first involves physics-informed neural networks (PINNs), which incorporate governing physical laws into the training process. The second focuses on operator learning methods—such as Fourier Neural Operators and Deep Operator Networks—that learn mappings between input and output functions. The third encompasses multi-operator learning and foundation models, including context-based operator networks, which offer a unified framework for solving both forward and inverse problems across diverse systems. By highlighting representative methods and their capabilities, this work aims to chart the recent progress in AI-based numerical solvers and outline future research directions in this rapidly evolving field.</p> Graphical Abstract <p></p>