The field of autonomous vehicle dynamics and safe navigation is rapidly advancing, with a focus on developing innovative methods for modeling and controlling complex systems. One of the key trends in this area is the integration of data-driven approaches, such as Koopman operator theory, with physical models to improve the accuracy and efficiency of simulations. Another important direction is the development of control barrier functions and Model Predictive Control (MPC) formulations to ensure safe navigation in dynamic environments. Additionally, researchers are exploring the application of deep learning techniques, such as physics-informed neural networks and graph neural networks, to improve the performance of traditional numerical methods. These advances have the potential to significantly enhance the safety and efficiency of autonomous vehicles and other complex systems. Noteworthy papers in this area include: Physics-Informed Adaptive Deep Koopman Operator Modeling for Autonomous Vehicle Dynamics, which introduces a physics-informed approach to improve the accuracy of Koopman operator approximation, and Efficient n-body simulations using physics informed graph neural networks, which presents a novel approach for accelerating n-body simulations using graph neural networks.