 We developed a method for efficiently computing reachable sets and forward invariant sets for continuous time systems with dynamics that include unknown components. The method relies on the theory of mixed monotone systems, which allows us to formulate an efficient algorithm for computing a hyper-rectangular set that over-approximates the reachable set of the system. Additionally, we derived a method for satisfying our main assumption by modeling the unknown components of state-dependent Gaussian processes, providing bounds that are correct with high probability. This enables us to compute reachable sets and forward invariant sets for systems up to moderately high dimensions that are subject to low-dimensional uncertainty modeled as Gaussian processes, a class of systems that often appears in practice. This article was authored by Michael Enki-Chao, Matthew Block, and Samuel Cougan.