Rather than alone or in dense clusters, most galaxies are found near a few others, in what astronomers call galaxy groups. Because of their ubiquity, they are important tracers of the underlying dark matter distribution. As such, they can be reliable tools for confronting predictions from cosmology. However, this can only happen if the complex gas and stellar properties of these systems are well understood. A collaboration between researchers at the University of Colorado at Boulder and Yale University will study the properties of galaxies in groups using computer simulations and Machine Learning methods. As part of the project, the researchers will expand the Telescope Prediction Shop, an undergraduate research program that will support students from the two campuses with the goal of fostering their advancement into STEM careers. A theoretical exploration of galaxy groups using a vast array of cosmological hydrodynamic simulations enhanced by Machine Learning emulators will be performed. The goal of the program is to better understand the processes of star formation, stellar feedback, chemical enrichment, and AGN feedback within galaxies in groups so that the groups may be used as reliable signposts for precision cosmology. The methodology includes using nearly 2000 state-of-the-art the volume and zoom simulations exploring 35 parameters to create synthetic X-ray observations and lightcone simulations probing groups out to z~2. This work will help to determine why scali