The recent developments in the research area of reduced-order modeling (ROM) and wave propagation simulation are significantly advancing the field, particularly in the context of parameter-dependent systems and Hamiltonian dynamics. Innovations in ROM techniques are being tailored to handle complex, nonlinear systems, with a focus on preserving essential structural properties such as symplecticity in Hamiltonian systems. This is achieved through the integration of machine learning techniques, such as symplectic autoencoders, which ensure that the reduced models maintain the inherent structure of the original systems. Additionally, advancements in space-time model reduction methods are demonstrating superior accuracy and efficiency, leveraging spatiotemporal correlations to enhance predictive capabilities. In the realm of wave propagation, there is a growing emphasis on developing methods that can simulate complex media and boundary conditions accurately, with notable progress in combining local interaction simulation approaches with perfectly matched layers. Furthermore, the creation of synthetic datasets for acoustic wave propagation is being facilitated by specialized libraries, which are crucial for training machine learning models in the absence of real-world data. These developments collectively indicate a shift towards more sophisticated and computationally efficient modeling techniques that can handle the intricacies of modern scientific and engineering challenges.