Digital twins for type 1 diabetes (T1D) aim to replicate the physiological responses of individual patients using mathematical models, enabling personalized and adaptive treatment. A critical step in this approach is the twinning procedure, i.e., the estimation of patient-specific parameters that allow the model to accurately mimic glucose-insulin dynamics under varying conditions such as meals, insulin injections, and physical activity.

This thesis investigates and compares multiple advanced inference methodologies for improving the twinning procedure within a state-of-the-art digital twin framework tailored for T1D patients. The focus will be on evaluating the effectiveness, robustness, and computational efficiency of the following approaches:

• Maximum a Posteriori (MAP) estimation, which offers a fast and deterministic approach to parameter identification by optimizing the posterior distribution.

• Markov Chain Monte Carlo (MCMC) methods, which provide asymptotically exact samples from the posterior and allow full uncertainty quantification, albeit at higher computational cost.

• Simulation-Based Inference (SBI) techniques, including likelihood-free methods that leverage forward simulations and machine learning to approximate the posterior, offering scalability and flexibility.

• Liquid Time-Constant Neural Networks (LTC-NN), a recent class of models that use deep learning to capture time-dependent latent dynamics, potentially enabling more expressive and data-driven representations of patient physiology.

The thesis will involve the development and implementation of these methods in a unified experimental pipeline. Performance will be assessed using synthetic data generated from the virtual patient models as well as real-world clinical data where available. Evaluation metrics will include predictive accuracy, convergence diagnostics, uncertainty calibration, and computational efficiency.