Abstract
Hybrid modelling is widely employed in chemical engineering to generate highly accurate predictions. Such an approach merges first-principle modelling with machine learning techniques to identify and model the epistemic uncertainty from experimental data. Despite its advantages, this still requires cross-domain competencies that are difficult to find in the chemical industry and high human involvement. The possibility of automating the identification and training model would be significantly beneficial for the widespread adoption of hybrid modelling methodology within the chemical industry. This work presents a novel algorithm for the automatic identification of hybrid models (HMs) starting from the first-principle representation of the system, described by differential equation sets. The methodology formulates the problem as mixed-integer programming, identifying the equation running under uncertainty, identifying the machine learning model hyperparameters, and training the latter. The Differential Evolution algorithm drives the identification and training tasks. The methodology is validated in three cases, namely a dynamic reaction system, a dynamic bioreactor and a Lotka-Volterra oscillator deviated with polynomial or MRF equation on different levels, generating 14 validation cases. On all of them, the model correctly identifies the position of the uncertainty and the functional form to approximate it. The methodology returns automatically trained HMs with a mean absolute percentage error in the range of 10%, which is in line with the experimental error of the data. The methodology presented in this work presents a step toward the automatic generation of HMs for dynamic systems and the widespread of this technology in the chemical industry.