A requirement of Smart Grids is the ability to predict the energy consumption patterns of their users. In the residential domain, this is usually not feasible due to the inability of the grid to dialog with (legacy) domestic appliances. To overcome this issue Non Intrusive Load Monitoring (NILM) was introduced, a task in which a predictor is used to disaggregate household power consumption. Many of the newer approaches make use of Neural Networks to accomplish this task, due to their superior ability to detect patterns in temporal (thus sequential) data. These models unfortunately require a huge amount of data to achieve good performance, and have the tendency to overfit the training data, making them difficult to predict future consumptions. For these reasons, adapting them to optimally predict a (future) house’s consumption requires expensive and often prohibitive data collection phases. We propose a solution in the form of a neuro-symbolic framework that refines neural network predictions via a constrained optimization problem modelling the characteristics of the appliances of a house. This combined approach achieves superior performance with respect to the neural network alone over two out of five appliances and comparable results for the remaining ones, without requiring further training data.