Two-photon lithography (TPL) is a direct laser writing process that enables the fabrication of cm-scale complex three-dimensional polymeric structures with submicrometer resolution. In contrast to the slow and serial writing scheme of conventional TPL, projection TPL (P-TPL) enables rapid printing of entire layers at once. However, process prediction remains a significant challenge in P-TPL due to the lack of computationally efficient models. In this work, we present machine learning-based surrogate models to predict the outcomes of P-TPL to >98% of the accuracy of a physics-based reaction-diffusion finite element simulation. A classification neural network was trained using data generated from the physics-based simulations. This enabled us to achieve computationally efficient and accurate prediction of whether a set of printing conditions will result in precise and controllable polymerization and the desired printing versus no printing or runaway polymerization. We interrogate this surrogate model to investigate the parameter regimes that are promising for successful printing. We predict combinations of photoresist reaction rate constants that are necessary to print for a given set of processing conditions, thereby generating a set of printability maps. The surrogate models reduced the computational time that is required to generate these maps from more than 10 months to less than a second. Thus, these models can enable rapid and informed selection of photoresists and printing parameters during process control and optimization.