An uncertainty-aware hybrid modelling approach using probabilistic machine learning

Hybrid modelling has caught renewed attention in many fields of engineering in the last two decades. By combining machine learning with first principles modelling, hybrid modelling is in many cases a more pragmatic modelling approach compared to first principles modelling, and at the same time a more robust alternative to data-driven modelling. However, quantifying uncertainty associated with hybrid models has not been investigated in detail thus far. Thereby, in practice, some models fail to reliably provide information for their performance under uncertainty. In this work, an integrated probabilistic modelling approach is presented for simultaneous modelling and uncertainty quantification using a hybrid model structure. The approach accounts for three types of uncertainty, including training data uncertainty, process stochasticity and model structure uncertainty. To demonstrate the advantages of this approach, the modelling strategy is highlighted through the modelling of a flocculation process. Here, mass and population balance models are combined with a probabilistic machine learning based kinetic model for estimating the particle phenomena kinetics. The model predictions are compared to predictions from a deterministic hybrid model counterpart.