Conditional universal differential equations capture population dynamics and interindividual variation in c-peptide...

Area of Science:

• Biomedical Systems Biology
• Machine Learning
• Computational Physiology

Background:

• Universal differential equations (UDEs) integrate mechanistic models with machine learning for data-driven discovery.
• Existing UDE training methods struggle with data heterogeneity and generalization across populations.
• Overfitting is a significant challenge for data-driven UDE models.

Purpose of the Study:

• To develop a novel conditional UDE (cUDE) framework to accommodate inter-individual data variation.
• To improve the generalizability of UDE models in heterogeneous populations.
• To apply cUDEs to model c-peptide production and derive analytical expressions.

Main Methods:

• Proposed a conditional UDE (cUDE) architecture with shared network structure/weights and individual-specific conditioning parameters.
• Trained cUDE models on diverse datasets representing normal glucose tolerance, impaired glucose tolerance, and type 2 diabetes mellitus.
• Utilized symbolic regression to derive a generalizable analytical expression from the trained cUDE model.

Main Results:

• The cUDE model accurately described postprandial c-peptide levels across different glucose tolerance groups.
• The conditional parameters effectively captured relevant inter-individual variations in c-peptide production.
• Symbolic regression successfully yielded a generalizable analytical expression for c-peptide dynamics.

Conclusions:

• Conditional UDEs offer a robust extension to the UDE framework for handling data heterogeneity in biomedical modeling.
• The cUDE approach enhances model generalizability and interpretability in complex biological systems.
• This work provides a new avenue for data-driven discovery in systems biology with improved patient stratification.