The field of predicting nonlinear dynamical systems is experiencing a significant shift towards the integration of machine learning and traditional numerical methods. Recent developments have focused on improving the accuracy and generalizability of predictions, particularly for complex systems governed by partial differential equations (PDEs). Notable advancements include the use of spectral methods, attention-based neural architectures, and physics-informed neural networks to model the evolution of nonlinear systems. These approaches have shown promise in achieving highly accurate long-term predictions, even with limited training data, and have the potential to revolutionize real-time prediction and control of complex dynamical systems. Some papers have proposed innovative frameworks that combine the strengths of different methods, such as using conditional video diffusion as a physics surrogate for spatio-temporal fields governed by PDEs, or leveraging mathematical artificial data to facilitate large-scale operator discovery. These advancements have far-reaching implications for various fields, including fluid dynamics, materials science, and biology. Noteworthy papers include: The Fourier Spectral Transformer Networks paper, which proposes a unified framework for efficient and generalizable nonlinear PDEs prediction. The Bridging Sequential Deep Operator Network and Video Diffusion paper, which presents a hybrid surrogate model that outperforms single-stage counterparts in predicting complex systems.