1. INTRODUCTION

2. DESCRIPTION OF THE MODELS
2.1. Illustris TNG
2.2. Santa Cruz Semi-Analytic Model
2.3. Molecular Hydrogen Fraction Recipes

3. ASPECS SURVEY OVERVIEW

4. RESULTS AND COMPARISON TO OBSERVATIONS
4.1.2. Mocked Results
4.2. The Evolution of the $H_{2}$ Mass Function
4.3. The $H_{2}$ Cosmic Density

5. DISCUSSION
5.1. Not Enough $H_{2}$ in Galaxy Simulations?
5.2. Field-to-Field Variance and Selection Effects for ASPECS
5.3. A Comparison to Earlier Works
5.4. Putting the Lack of $H_{2}$ in a Broader Picture

6. SUMMARY & CONCLUSIONS