  Stellar photospheric activity is known to limit the detection and
characterisation of extra-solar planets. In particular, the study of Earth-like
planets around Sun-like stars requires data analysis methods that can
accurately model the stellar activity phenomena affecting radial velocity (RV)
measurements. Gaussian Process Regression Networks (GPRNs) offer a principled
approach to the analysis of simultaneous time-series, combining the structural
properties of Bayesian neural networks with the non-parametric flexibility of
Gaussian Processes. Using HARPS-N solar spectroscopic observations encompassing
three years, we demonstrate that this framework is capable of jointly modelling
RV data and traditional stellar activity indicators. Although we consider only
the simplest GPRN configuration, we are able to describe the behaviour of solar
RV data at least as accurately as previously published methods. We confirm the
correlation between the RV and stellar activity time series reaches a maximum
at separations of a few days, and find evidence of non-stationary behaviour in
the time series, associated with an approaching solar activity minimum.
