English: A problem-specific Gaussian process prior ${\displaystyle u}$ is conditioned on partially-known physics, given by uncertain boundary conditions (BC) and a linear PDE, as well as on noisy physical measurements from experiment. The boundary conditions and the right-hand side of the PDE are not known but inferred from a small set of noise-corrupted measurements. The plots juxtapose the belief ${\displaystyle u\mid \cdots }$ with the true solution ${\displaystyle u^{\star }}$ of the latent boundary value problem.