  We present a novel approach for reconstructing the projected mass
distribution of clusters of galaxies from sparse and noisy weak gravitational
lensing shear data. The reconstructions are regularised using knowledge gained
from numerical simulations of clusters: trial mass distributions are
constructed from N physically-motivated components, each of which has the
universal density profile and characteristic geometry observed in simulated
clusters. The parameters of these components are assumed to be distributed
\emph{a priori} in the same way as they are in the simulated clusters. Sampling
mass distributions from the components' parameters' posterior probability
density function allows estimates of the mass distribution to be generated,
with error bars. The appropriate number of components is inferred from the data
itself via the Bayesian evidence, and is typically found to be small,
reflecting the quality of the simulated data used in this work. Ensemble
average mass maps are found to be robust to the details of the noise
realisation, and succeed in recovering the input mass distribution (from a
realistic simulated cluster) over a wide range of scales. We comment on the
residuals of the reconstruction and their implications, and discuss the
extension of the method to include strong lensing information.
