  The use of high-power industrial equipment, such as large-scale mixing
equipment or a hydrocyclone for separation of particles in liquid suspension,
demands careful monitoring to ensure correct operation. The fundamental task of
state-estimation for the liquid suspension can be posed as a time-evolving
inverse problem and solved with Bayesian statistical methods. In this paper, we
extend Bayesian methods to incorporate statistical models for the error that is
incurred in the numerical solution of the physical governing equations. This
enables full uncertainty quantification within a principled
computation-precision trade-off, in contrast to the over-confident inferences
that are obtained when all sources of numerical error are ignored. The method
is cast within a sequential Monte Carlo framework and an optimised
implementation is provided in Python.
