  With the ever-increasing availability of data, there has been an explosion of
interest in applying modern machine learning methods to fields such as modeling
and control. However, despite the flexibility and surprising accuracy of such
black-box models, it remains difficult to trust them. Recent efforts to combine
the two approaches aim to develop flexible models that nonetheless generalize
well; a paradigm we call Hybrid Analysis and modeling (HAM). In this work we
investigate the Corrective Source Term Approach (CoSTA), which uses a
data-driven model to correct a misspecified physics-based model. This enables
us to develop models that make accurate predictions even when the underlying
physics of the problem is not well understood. We apply CoSTA to model the
Hall-H\'eroult process in an aluminum electrolysis cell. We demonstrate that
the method improves both accuracy and predictive stability, yielding an overall
more trustworthy model.
