What is the story of galaxy formation – when, where, and how did these vast cosmic ecosystems assemble? How did they build-up their heavy elements, assemble their stellar populations, and grow their supermassive black holes? Armed with ultra-deep, ultra-broad photometric and spectroscopic surveys of the universe, we are in a better position to answer these questions than ever before. Yet these new data breathe new life into long-standing challenges in extragalactic observations: how do we simultaneously model all of these processes at once? In this talk I present recent progress made using the high-dimensional modeling of galaxy SEDs and galaxy populations. By including flexible, model-agnostic prescriptions for the complex physical processes in galaxies, we have produced qualitatively new and quantitatively distinct solutions for simple galaxy properties. These new solutions solve old problems, for example different measurements of the cosmic star formation rate density, or discrepancies between galaxy star formation rates and halo mass accretion rates. However, to date these models have only been applied to small samples due to their high computational requirements. I will present rapidly accelerating research into machine learning techniques which dramatically speed up inference, by factors of thousands to millions. I end by describing the near future where lightning-fast ML-powered inference techniques and massive large-scale surveys promise to open up entirely new research directions in extragalactic astronomy – for example, modeling the formation histories of tens millions of galaxies simultaneously, using unresolved galaxies as laboratories for exotic phases of stellar evolution, and accurately modeling their complex spatial structures.
