Identification of physiological parameters and missing inputs in glucose dynamics via PINN-constrained inference

Accurate glucose-insulin modeling under free-living conditions is challenged by incomplete or inaccurate input records, noisy continuous glucose monitoring data, and strong inter-individual physiological variability. These factors complicate reliable personalization and system identification. This study aims to develop a physiologically grounded identification framework capable of estimating subject-specific physiological parameters and unobserved exogenous inputs from partially observed data.

The proposed glucose latent input and parameter inversion (GLU-INVERT) framework extends the Bergman minimal model by incorporating additional physiological states and casting the identification task as a structured inverse problem with provable identifiability. A physics-informed learning mechanism embeds glucose and insulin dynamics as differentiable constraints, while an alternating optimization strategy estimates subject-specific physiological parameters and infers sparse latent meal correction signals.

Parameter estimates obtained by the proposed framework remained within established physiological ranges and exhibited reduced inter-subject variability, indicating improved identifiability under incomplete input information. As a secondary validation, the identified model was evaluated in a rolling-horizon forecasting setting with fixed parameters. From the 30-minute to the 120-minute prediction horizon, the proposed GLU-INVERT framework achieved the lowest mean absolute relative difference (MARD), increasing moderately from 8.8% to 24.1%, whereas alternative approaches showed larger increases from 10.3% to 30.0%. Over the same horizons, GLU-INVERT also attained the lowest root mean squared error (RMSE), rising from 0.69 to 1.80,mmol/L, compared with increases from 0.78 to 2.29,mmol/L for the alternatives. Performance improvements over the least-squares baseline were statistically significant across all prediction horizons (p<0.05) and degraded more slowly with increasing horizon length, indicating enhanced stability under data-limited conditions.

By addressing parameter uncertainty and missing input information, GLU-INVERT provides a robust and interpretable framework for physiological system identification under real-world data constraints. Forecasting performance is presented as a secondary validation of the identified model and highlights its potential utility for personalized glucose monitoring and decision support.