The continuous flow or `transport' of a macroscopic system of particles is a high dimensional problem and therefore often solved using reduced order models. This necessarily introduces unknown closure relations into these models. In this work, we present a machine learning approach to finding accurate closure relations utilising differentiable programming. As a case study, we consider the transport of photons and use a literature radiation transport test problem as a training dataset. We present novel ML closures for a number of reduced order models which out-perform their literature counterparts in both trained and unseen problems.