<p>The high computational cost of traditional numerical methods in differential equation analysis, particularly in computational fluid dynamics, remains an issue. While general-purpose artificial intelligence (AI) models have shown acceleration in steady-state analysis, they struggle with error accumulation when it comes to transient-state problems. Although scientific AI models can improve prediction accuracy, stability issues still arise when used as standalone solvers. To address these limitations, hybrid solvers have recently been proposed. Notably, residual-based physics-informed transfer learning (RePIT) and hybrid iterative numerical transferable solver (HINTS) have demonstrated that combining AI and traditional numerical techniques can improve computational speed while maintaining numerical stability. This study provides an overview of general and scientific AI models before introducing the latest hybrid approaches, offering practical insights into the future of differential equation analysis.</p> Graphical abstract <p></p>