We present a framework for enhancing Gaussian process regression machine learning models with a priori knowledge derived from models of the transmission physics in optical networks. This is done by framing the regression problem as multi-task learning, in which both the measured data and targets derived from a physical model of the system are used to optimise the kernel hyperparameters. We discuss the theoretical assumptions made and the validity of the approach. It is demonstrated that physics informed Gaussian processes facilitate Bayesian inference with fewer data points than standard Gaussian processes, opening up application areas in which measurements are expensive. The transparency, interpretability and explainability of the proposed technique and the subsequent increased likelihood of adoption by industry are discussed.