Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes

Continuous glucose monitoring (CGM) provides a dense view of daily metabolic physiology, yet existing generic time-series and CGM-specific foundation models often encode glucose traces as entangled single-stream sequences, leaving the distinct temporal structure of glycemic dynamics only implicitly modeled. We present GlucoFM, a lightweight CGM foundation model that aligns irregular recordings to a 24-hour chronological grid, preserves observation masks, and decomposes glucose dynamics into slow physiological state and transient event streams, capturing low-frequency glycemic baselines and short-term deviations that may reflect acute physiological responses or sensor artifacts. GlucoFM is pretrained on 109,066 hours of unlabeled CGM recordings from 477 subjects with two complementary objectives: masked contextual latent prediction over fused daily representations and temporal dynamics prediction over state and event streams. Across four diverse cohorts and seven clinical prediction tasks, GlucoFM achieves the strongest subject-disjoint linear-probing performance among evaluated baselines, improving average PR-AUC by 4.1 points over the best CGM-specific foundation model. Its gains are most pronounced on core metabolic outcomes, leading PR-AUC on all diabetes-risk and $β$-cell dysfunction tasks and on 3 of 4 insulin-resistance tasks. GlucoFM also achieves the best overall cross-dataset transfer performance and strong few-shot adaptation among evaluated methods, and consistent gains when aggregating multiple days for subject-level prediction, highlighting physiology-aware decomposition as an effective inductive bias for transferable CGM representation learning.

Accurate long-horizon glucose forecasting is critical for automated insulin delivery systems, which help people with type 1 diabetes (T1D) manage their glucose and avoid dangerous hypoglycemia. However, standard recursive long short-term memory (LSTM) networks suffer from systematic negative bias at longer horizons due to error compounding, while purely mechanistic ordinary differential equation (ODE) models fail to generalize across individuals when parameterized at the population level. We propose PhysioSeq2Seq, a hybrid architecture that combines patient-specific physiological modeling with a sequence-to-sequence (Seq2Seq) LSTM. For each glucose segment, twin matching searches a population of 300 parameterized digital twins to identify the best-fitting physiological match from a 3-hour continuous glucose monitoring (CGM) history. The 10 internal ODE state variables of the matched twin are injected as exogenous covariates into both the encoder and decoder of the Seq2Seq LSTM. This simultaneous 48-step prediction strategy eliminates recursive error compounding, while the ODE features provide a physics-grounded constraint that bounds long-horizon drift within physiologically plausible ranges. PhysioSeq2Seq was trained on CGM and insulin data from 348 participants in the Type 1 Diabetes Exercise Initiative (T1DEXI) dataset and evaluated on 74 held-out participants. At the 240-minute horizon, PhysioSeq2Seq achieves a mean absolute error of 39.28 mg/dL and a mean error of -10.62 mg/dL, reducing bias by 13.89 mg/dL over the recursive LSTM and reducing mean absolute error by 28.62 mg/dL over the ODE-based digital twin. These results show that eliminating architectural feedback and injecting patient-matched physiological states is an effective and clinically meaningful strategy for long-horizon glucose forecasting in T1D.

Effective diabetes management requires continuous monitoring of glycemic levels. Clinically, glycemic control is assessed using metrics such as Time in Range (TIR), Time Below Range (TBR), and Time Above Range (TAR), typically derived from continuous glucose monitoring (CGM). However, many patients rely on self-monitoring of blood glucose (SMBG) due to the high cost and limited accessibility of CGM. Unlike CGM, SMBG provides sparse and irregular measurements, making accurate estimation of these metrics challenging. Conventional supervised learning approaches struggle under such sparsity, leading to poor generalization and unstable performance. To address this, we propose PACD-Net, a self-supervised contrastive knowledge distillation framework for estimating glycemic control from SMBG. Pseudo-SMBG samples with richer temporal coverage are used as teacher signals to guide learning from sparse observations. In addition, multi-view contrastive learning enforces representation consistency across diverse sampling patterns. The model adopts a hybrid Swin Transformer-CNN backbone to capture temporal dependencies in sparse SMBG sequences. Experimental results demonstrate that PACD-Net consistently outperforms existing methods in estimating TAR, TIR, and TBR from real-world SMBG data, achieving improved accuracy as well as enhanced stability and generalization under extremely sparse observation settings. The proposed framework provides a practical tool for clinical SMBG interpretation and offers a generalizable approach for learning from sparse and irregularly sampled sensor data in broader applications.