Deep learning has recently become an important part of nanophotonic device design, with many researchers leveraging the power of neural networks to aid in inverse-design analysis. Acting as surrogate models for full-wave solvers, neural networks are now employed to develop new metasurface elements and gain insight into the underlying physics which dictate their behavior. A new avenue of discovery, which has been facilitated by the recent developments in deep learning, lies in the domain of metasurface robustness, a subject that presents many challenges to traditional solvers. Characterizing even relatively simple designs with a full-wave solver may be computationally expensive enough to make optimization challenging or even intractable. On the other hand, robustness must be measured by introducing some form of tolerance analysis into an optimization. Structures must be perturbed many times over, perhaps even in an exhaustive fashion. When the process is further complicated by considering complex design parameterizations (with many degrees of freedom), these full-wave optimizations are no longer tractable. However, deep neural networks can help to counter these challenges owing to their GPU speedup and powerful learning characteristics. By evaluating many full-wave metasurface designs ahead-oftime and investing them into neural network training, the network can then be used in tolerance analysis for substantial speedups down the road. This work showcases how we designed a suitable neural network for this purpose, as well as several studies conducted using this deep learning platform in this important area of metasurface robustness.