Power distribution networks are changing, and the relatively simple infrastructure that existed at the last mile is now being challenged by the integration of low-carbon generation, energy storage and weather dependent loads that it was not originally designed for. The scale of this asset portfolio is such that extensive monitoring is out of the question in terms of cost and even if it wasn't, there are commercial and regulatory obstacles to overcome. Alternatively, understanding of distribution network loads can be improved through learning across the sparsely available data and applying these learned characteristics to unobservable behaviours and networks. Here, a methodology which uses a combination of machine learning models and power system modelling to infer unknown behaviours on power distribution networks which are too extensive to monitor, is presented. At the premises end, advanced clustering models are used to identify recurring load behaviour predicates, including artefacts that may be inferred as behind the meter generation. At the substation end, a means of inferring the composition of subpopulations of load behaviours is used to estimate the total load and therefore the potential losses on the feeder. In combination, this approach can reduce the need for expensive monitoring solutions in the parts of the network where net zero achievements are challenged.