Identifiability and interpretability of hybrid, gray-box models

Model identifiability concerns the uniqueness of uncertain model parameters to be estimated from available process data and is often thought of as a prerequisite for physical interpretability of the parameters in a mechanistic model. Nevertheless, model identifiability is rarely accomplished in practice due to both stochastic and deterministic uncertainties: lack of sufficient variability in the data, noisy measurements, erroneous model structure, stochasticity and locality of the optimization algorithm, initial values, and even the parameter of the true underlying process. For gray-box, hybrid models, model identifiability is even less obtainable due to a higher number of parameters compared to mechanistic models. We illustrate by means of an industrial case study, modeling of a production choke valve in a petroleum well, how physical interpretation of the physical model parameters may be preserved for non-identifiable models by utilizing parameter regularization in the estimation problem. Further, we design and train interpretable gray-box choke models on historical process data from six wells on the petroleum asset Edvard Grieg. Comparing the prediction performance of the gray-box model to a mechanistic model for the median well shows a significant increase in prediction accuracy.