Physics-Informed Prediction of Uncertain Glucose Dynamics: Integrating Wong-Zakai Corrected Stochastic Differential Equations with Machine Learning

Failure to adequately monitor blood glucose exposes people with diabetes to acute and chronic complications driven by recurrent hypoglycemia and hyperglycemia, requiring technologies that enable reliable glycemic assessment. Non-invasive glucose monitoring forecasting supports real-time decision support and safer insulin therapy. However, since glucose dynamics are governed by nonlinear physiology, continuous-sensing delays and noise, and partially observed exogenous inputs such as meals, stress, and physical activity, an accurate prediction remains challenging. This paper proposes a hybrid, physics-informed methodology for predicting uncertain glucose dynamics that couples mechanistic glucose-insulin modeling with flexible machinelearning components. The approach embeds known physiological structure directly into the learning process, while data-driven modules capture residual effects, patient-specific variability, and unmeasured disturbances. To represent intrinsic randomness and improve physical fidelity, we formulate a stochastic glucose-insulin model based on Wong-Zakai corrected stochastic differential equations, enabling a more realistic description of nonlinear relationships such as insulin concentration-dependent degradation as well as the presence of multiplicative noise. We validate the proposed methodology on real-world continuous glucose monitoring data, benchmarking against a traditional purely data-driven baseline. The results highlight the value of stochastic, physics-informed hybrid modeling as a practical path toward interpretable and reliable glucose prediction under real-life variability.