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

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

Multiple shooting with neural differential equations

Neural differential equations have recently emerged as a flexible data-driven/hybrid approach to model time-series data. This work experimentally demonstrates that if the data contains oscillations, then standard fitting of a neural differential equation may give flattened out trajectory that fails to describe the data. We then introduce the multiple shooting method and present successful demonstrations of this method for the fitting of a neural differential equation to two datasets (synthetic and experimental) that the standard approach fails to fit. Constraints introduced by multiple shooting can be satisfied using a penalty or augmented Lagrangian method.