  We study the Bayesian inverse problem of inferring the permeability of a
porous medium within the context of a moving boundary framework motivated by
Resin Transfer Molding (RTM), one of the most commonly used processes for
manufacturing fiber-reinforced composite materials. During the injection of
resin in RTM, our aim is to update our probabilistic knowledge of the per-
meability of the material by inverting pressure measurements as well as
observations of the resin moving domain. We consider both one-dimensional and
two-dimensional forward models for RTM. Based on the analytical solution for
the one-dimensional case, we prove existence of the sequence of posteriors that
arise from a sequential Bayesian formulation within the infinite-dimensional
framework. For the numerical characterisation of the Bayesian posteriors in the
one-dimensional case, we investigate the application of a fully-Bayesian
Sequential Monte Carlo method (SMC) for high-dimensional inverse problems. By
means of SMC we construct a benchmark against which we compare performance of a
novel regularizing ensemble Kalman algorithm (REnKA) that we propose to
approximate the posteriors in a computationally efficient manner under
practical scenarios. We investigate the robustness of the proposed REnKA with
respect to tuneable param- eters and computational cost, and display advantages
of REnKA compared with SMC with a small number of particles. We further apply
REnKA to investigate, in both the one-dimensional and two-dimensional settings,
practical aspects relevant to RTM which include the effect of pressure sensors
configuration and the observational noise level in the uncertainty in the
log-permeability quantified via the sequence of Bayesian posteriors.
