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To operate process engineering systems in a safe and reliable manner,predictive models are often used in decision making. In many cases, these aremechanistic first principles models which aim to accurately describe theprocess. In practice, the parameters of these models need to be tuned to theprocess conditions at hand. If the conditions change, which is common inpractice, the model becomes inaccurate and needs to be re-tuned. In this paper,we propose a hybrid modeling machine learning framework that allows tuningfirst principles models to process conditions using two different types ofBayesian Neural Networks. Our approach not only estimates the expected valuesof the first principles model parameters but also quantifies the uncertainty ofthese estimates. Such an approach of hybrid machine learning modeling is notyet well described in the literature, so we believe this paper will provide anadditional angle at which hybrid machine learning modeling of physical systemscan be considered. As an example, we choose a multiphase pipe flow process forwhich we constructed a three-phase steady state model based on the drift-fluxapproach which can be used for modeling of pipe and well flow behavior in oiland gas production systems with or without the neural network tuning. In thesimulation results, we show how uncertainty estimates of the resulting hybridmodels can be used to make better operation decisions.

Hybrid Machine Learning Modeling of Engineering Systems -- A Probabilistic Perspective Tested on a Multiphase Flow Modeling Case Study