Numerical strategy for model correction using physical constraints

In this paper we present a strategy for correcting model deficiency using observational data. We first present the model correction in a general form, involving both external correction and internal correction. The model correction problem is then parameterized and casted into an optimization problem, from which the parameters are determined. More importantly, we discuss the incorporation of physical constraints from the underlying physical problem. Several representative examples are presented, where the physical constraints take very different forms. Numerical tests demonstrate that the physics constrained model correction is an effective way to address model-form uncertainty.