The recent developments in the research area of control systems and partial differential equations (PDEs) have shown a significant shift towards leveraging advanced machine learning techniques and innovative control strategies. A notable trend is the integration of neural operators and diffusion models to enhance the robustness and efficiency of control systems, particularly in handling complex and high-dimensional states. These methods are being applied to a variety of challenging physical systems, including those with abrupt changes and varying resolutions, demonstrating superior performance in both simulation and control tasks. Additionally, there is a growing focus on distributed and learning-based control schemes, which aim to address the scalability and adaptability challenges in multi-agent systems and real-time applications. These advancements are paving the way for more precise and efficient control in dynamic systems, with applications ranging from autonomous spacecraft rendezvous to mitigating induced seismicity in underground reservoirs. Notably, the use of wavelet diffusion neural operators and distributed deep Koopman learning algorithms are particularly innovative, offering significant improvements in handling abrupt changes and long-term dependencies, as well as enabling precise dynamics learning and control in large-scale systems.