Application of PINN in Endocrine Parameter Discovery: Inferring Hidden Physiological Parameters from Observed Data

This project aims to use Physics-Informed Neural Networks (PINN) to solve inverse problems in endocrinology, recover hidden physiological parameters (such as glucose clearance rate) from sparse and noisy clinical observation data (such as blood glucose concentration), realize the practical application of scientific machine learning in computational endocrinology, and provide a new tool for personalized medicine.

In the biomedical field, key physiological parameters (such as insulin sensitivity, hormone degradation constants) cannot be directly measured, but are crucial for understanding disease mechanisms and personalized treatment. Traditional machine learning excels at predicting observable variables, but struggles to answer the inverse problem of 'which parameters generate the observed data'—this is the core challenge of this project.

Physics-Informed Neural Networks (PINN) embed physical laws into the training process, balancing data consistency and physical laws. This project uses a simplified blood glucose regulation model: dG/dt = -p₁(G - G_b) - XG, with the goal of estimating the hidden parameter p₁ (glucose clearance parameter) rather than just reconstructing the blood glucose trajectory.

The network uses a fully connected structure, taking p₁ as a trainable variable and outputting the blood glucose trajectory G(t), insulin action state X(t), and parameter p₁. The composite loss function is: Total Loss = L_data (MSE between predicted and observed blood glucose) + λ×L_physics (MSE of ODE residuals), balancing data fidelity and physical constraints.

The experiment uses synthetic sparse and noisy blood glucose data to simulate clinical scenarios. After training the PINN, the hidden parameter was successfully recovered: the true p₁=0.025, and the estimated value was approximately 0.025; the reconstructed blood glucose trajectory was highly consistent with the observed data and conformed to physiological laws.

The innovations include inverse problem solving, sparse noisy data processing, physical constraint integration, and interpretability. Application directions include diabetes monitoring (estimating parameters from CGM data), personalized medicine (learning patient-specific parameters), etc.

The project is implemented in Python, mainly relying on PyTorch (deep learning framework), NumPy (numerical computation), and Matplotlib (visualization). The code structure is clear, including a complete PINN implementation, result visualization, and documentation.

This project demonstrates the strong potential of scientific machine learning in the biomedical field, integrating data-driven and mechanistic modeling. Future expansions can include uncertainty quantification, comparison with traditional methods, etc., to promote the development of precision medicine.