Invasive rodent populations pose a threat to biodiversity across the globe. When confronted with these invaders, native species that evolved independently are often defenseless. CRISPR gene drive systems could provide a solution to this problem by spreading transgenes among invaders that induce population collapse, and could be deployed even where traditional control methods are impractical or prohibitively expensive. Here, we develop a high-fidelity model of an island population of invasive rodents that includes three types of suppression gene drive systems. The individual-based model is spatially explicit, allows for overlapping generations and a fluctuating population size, and includes variables for drive fitness, efficiency, resistance allele formation rate, as well as a variety of ecological parameters. The computational burden of evaluating a model with such a high number of parameters presents a substantial barrier to a comprehensive understanding of its outcome space. We therefore accompany our population model with a meta-model that utilizes supervised machine learning to approximate the outcome space of the underlying model with a high degree of accuracy. This enables us to conduct an exhaustive inquiry of the population model, including variance-based sensitivity analyses using tens of millions of evaluations. Our results suggest that sufficiently capable gene drive systems have the potential to eliminate island populations of rodents under a wide range of demographic assumptions, though only if resistance can be kept to a minimal level. This study highlights the power of supervised machine learning to identify the key parameters and processes that determine the population dynamics of a complex evolutionary system.