Abstract
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 article, 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 optimized implementation is provided in Python.
Acknowledgments
The authors are grateful for detailed suggestions from the associate editor and two anonymous reviewers. For the numerical results reported in Section 3, we thank T. J. Sullivan for the use of computing facilities at the Freie Universität Berlin, funded by the Excellence Initiative of the German Research Foundation.