Stable Compartmental Recurrent Neural Networks for Glucose–Insulin Dynamics Modeling in the Artificial Pancreas Framework

Models of glucose-insulin dynamics are essential in treating type 1 diabetes. Yet, the adoption of advanced methods such as Recurrent Neural Networks (RNNs), which provide superior predictive accuracy over traditional linear models, remains limited in safety-critical applications due to their black-box nature and inherent lack of theoretical guarantees. To overcome these limitations, recent advancements introduced the compartmental RNN for glucose prediction. This approach embeds the topology of the physiological system into the network, eliminating unphysiological cross-talk between insulin and meal effects, typical of purely black-box structures. However, these architectures still rely on standard RNNs, like gated recurrent unit networks, i.e., models that lack formal stability guarantees. In this work, we bridge this gap by introducing the stable compartmental RNN. Our proposal leverages chaos-free networks as internal compartmental units, ensuring that the resulting model inherently satisfies input-to-state stability by design, requiring no complex parametric constraints during network training. Numerical validation on the in silico UVA/Padova simulator confirms that the proposed architecture achieves high predictive accuracy while providing formal stability guarantees.