In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional free space wave equation. In a recent article, we obtained promising covariance expressions for this equation: we now explore the potential applications of these formulas. We first study the particular cases of stationarity, radial symmetry and point source, for which significant simplifications arise. We next show that the true-angle multilateration method for point source localization, as used in GPS systems, is naturally recovered by our GPR formulas in the limit of the small source radius. Additionally, we show that this GPR framework provides a new answer to the ill-posed inverse problem of reconstructing initial conditions for the wave equation from a limited number of sensors, and simultaneously enables the inference of physical parameters from these data. We finish by illustrating this ``physics informed'' GPR on a number of practical examples.