Theoretical efforts to understand and model galaxy formation are mostly beyond the analytical realm, where they divide into semi-analytic models and cosmological simulations. These two approaches have been converging in recent years, as the practitioners of cosmological hydrodynamic simulations are using more detailed "recipes" for star formation, supernova feedback, and winds and in some cases have claimed grandiose results from purely N-body simulations with many semi-analytic recipes added (e.g. Springel et al. 2005). For examples of state-of-the-art cosmological hydrodynamic simulations of high-redshift galaxies and AGN, see Nagamine, Springel, & Hernquist (2004) and Di Matteo, Springel, & Hernquist (2005).
Semi-analytic models reproduce observations moderately well but have yet to demonstrate much success in predicting future observations, making them more of a tool for interpreting results than theoretical models in the classic sense. Somerville, Primack, & Faber (2001) tuned their models to reproduce galaxy properties at z = 0 and found one of their models to be in good agreement with the dust-corrected points at z > 2 in the cosmic SFRD diagram. However, as mentioned above, semi-analytic models for infall, merging, and winds are highly uncertain and it is not clear if observations of the cosmic density of neutral gas and the missing metals problem are consistent with the predictions. Similar scatter is seen in theoretical predictions of the cosmic stellar mass density.