Learning, fast and slow: a two-fold algorithm for data-based model adaptation

This article addresses the challenge of adapting data-based models over time. We propose a novel two-fold modelling architecture designed to correct plant-model mismatch caused by two types of uncertainty. Out-of-domain uncertainty arises when the system operates under conditions not represented in the initial training dataset, while in-domain uncertainty results from real-world variability and flaws in the model structure or training process. To handle out-of-domain uncertainty, a slow learning component, inspired by the human brain's slow thinking process, learns system dynamics under unexplored operating conditions, and it is activated only when a monitoring strategy deems it necessary. This component consists of an ensemble of models, featuring (i) a combination rule that weights individual models based on the statistical proximity between their training data and the current operating condition, and (ii) a monitoring algorithm based on statistical control charts that supervises the ensemble's reliability and triggers the offline training and integration of a new model when a new operating condition is detected. To address in-domain uncertainty, a fast learning component, inspired by the human brain's fast thinking process, continuously compensates in real time for the mismatch of the slow learning model. This component is implemented as a Gaussian process (GP) model, trained online at each iteration using recent data while discarding older samples. The proposed methodology is tested on a benchmark energy system referenced in the literature, demonstrating that the combined use of slow and fast learning components improves model accuracy compared to standard adaptation approaches.