Members of the TAMIDS Scientific Machine Learning Lab and TAMIDS Digital Twin Lab have developed a new graduate course Physics-based and Data-Driven Reduced-Order Modeling for Engineering Systems with a focus on methods to speed up engineering workflows by mitigating the need for expensive computations in multiphysics and other engineering contexts. Applications include: reservoir simulation, production optimization, complex multiphase flow simulation, neutron diffusion, coupled neutronics/thermal-hydraulics, and nuclear heat transfer. The course is intended primarily for graduate students interested in computational science / engineering application. The course materials are complemented by a balanced set of theoretical, algorithmic, and MATLAB/Python computer programming assignments. Invited lectures from researchers and professionals in model reduction will be given as time permits. Prospective students can contact the instructors Dr. Eduardo Gildin (firstname.lastname@example.org) or Dr. Jean Ragusa (email@example.com) for more information on the class.