Thermal modeling of thin-layer bread via neural networks: Experimental validation in a Sardinian bakery

This paper presents neural network-based methods for modeling the cooling behavior of Sardinian flatbreads, validated through experimental data collected in a Sardinian bakery. Building upon previous research on the drying-cooling dynamics of pane Carasau, which identified the Verma model as one of the most suitable thin-layer models for flatbreads, a data-driven framework is developed to tune the Verma model coefficients. Given the Industry 5.0-oriented operational setting of the bakery, the proposed framework is conceived as a human-centric decision-support tool that provides operators with scenario-dependent predictions of cooling behavior under varying initial and ambient conditions, thereby supporting informed adjustments of process settings while preserving human oversight. The goal is to learn how the model coefficients vary with boundary conditions – such as initial temperature and ambient conditions – thereby enhancing model accuracy and generalization in real industrial settings. Two identification strategies are proposed: (i) a physics-informed approach, which embeds the Verma law directly into the network training process, and (ii) a supervised approach, where the network learns the Verma model parameters from labeled cooling curves. Real thermal imaging measurements acquired in an industrial bakery are used for both training and validation. Results show that both approaches perform effectively and with similar performance, thus demonstrating the advantages of integrating physical modeling with data-driven learning.