  The automated localisation of damage in structures is a challenging but
critical ingredient in the path towards predictive or condition-based
maintenance of high value structures. The use of acoustic emission time of
arrival mapping is a promising approach to this challenge, but is severely
hindered by the need to collect a dense set of artificial acoustic emission
measurements across the structure, resulting in a lengthy and often impractical
data acquisition process. In this paper, we consider the use of
physics-informed Gaussian processes for learning these maps to alleviate this
problem. In the approach, the Gaussian process is constrained to the physical
domain such that information relating to the geometry and boundary conditions
of the structure are embedded directly into the learning process, returning a
model that guarantees that any predictions made satisfy physically-consistent
behaviour at the boundary. A number of scenarios that arise when training
measurement acquisition is limited, including where training data are sparse,
and also of limited coverage over the structure of interest. Using a complex
plate-like structure as an experimental case study, we show that our approach
significantly reduces the burden of data collection, where it is seen that
incorporation of boundary condition knowledge significantly improves predictive
accuracy as training observations are reduced, particularly when training
measurements are not available across all parts of the structure.
