Controlled latent ODE-RNN for continuous-time blood glucose modeling : Representation learning, factual and counterfactual dietary predictions

Details

Supervisors

Symul, Laura

Faculty

Faculté des sciences

Degree label

Master [120] en science des données, orientation statistique, à finalité spécialisée

Abstract

enModeling and predicting individual continuous-time blood glucose trajectories is a challenging problem at the intersection of dynamical systems modeling and precision medicine. The underlying process is continuous, governed by non-linear physiological dynamics, perturbed by discrete meal intake, and observed only through noisy, irregularly sampled measurements. While explicit mechanistic models have been proposed, some may make assumptions about the dynamics that are difficult to experimentally validate. This motivates turning to data-driven approaches relying on overparametrized models. Specifically, Neural differential equation approaches handle irregularly sampled data while enjoying the toolbox of dynamical systems as well as the expressivity of neural networks. In particular, the Latent ODE-RNN of Rubanova et al. (2019), a Deep State-Space model, provides a principled uncertainty quantification framework, yet lacks an explicit mechanism for exogenous meal inputs, which is essential for blood glucose modeling. In this work, we introduce CLODE (Controlled Latent ODE-RNN), a generative framework that extends the Latent ODE-RNN by incorporating meal intake as a time-varying exogenous control signal into the latent dynamics. Two meal signal parametrizations are compared: a Dirac impulse and a β-kernel distributing carbohydrate absorption over a physiologically plausible ingestion window. CLODE was evaluated on two simulated populations of 500 in silico individuals, one physiologically homogeneous and one exhibiting inter-individual variability, and compared against the ODE-LSTM (Lechner and Hasani, 2020; Fitzgerald et al., 2023) and the Latent ODE-RNN models. CLODE (β-kernel) substantially outperformed both baselines on factual forecasting and counterfactual prediction across three dietary scenarios. Latent space analysis further suggested that explicitly separating exogenous meal inputs from latent dynamics encourages the emergence of physiologically structured representations, though alignment with ground-truth parameters remained low. We conjecture that conditioning on longer observation windows, conditioning on additional inputs that would be available in realistic clinical conditions, or refining the architecture would allow to better disambiguate individual physiological profiles. Overall, these results provide encouraging evidence that controlled latent dynamics constitute a promising direction for personalized glucose modeling, dietary planning, or any "homeostasis-and-perturbation" system where individual-specific latent dynamics are perturbed by exogenous inputs and observed through noisy, irregularly sampled measurements.