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The use of high-power industrial equipment, such as large-scale mixingequipment or a hydrocyclone for separation of particles in liquid suspension,demands careful monitoring to ensure correct operation. The fundamental task ofstate-estimation for the liquid suspension can be posed as a time-evolvinginverse problem and solved with Bayesian statistical methods. In this paper, weextend Bayesian methods to incorporate statistical models for the error that isincurred in the numerical solution of the physical governing equations. Thisenables full uncertainty quantification within a principledcomputation-precision trade-off, in contrast to the over-confident inferencesthat are obtained when all sources of numerical error are ignored. The methodis cast within a sequential Monte Carlo framework and an optimisedimplementation is provided in Python.

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment