Comparative Study of PINN and Classical Numerical Methods in Diabetes Blood Glucose Modeling

Source: Jana-Hazem (GitHub Project: Diabetes-glucose-tolerance, Link: https://github.com/Jana-Hazem/Diabetes-glucose-tolerance, Published on: June 10, 2026)

Core Research: Combines mathematical modeling, classical numerical methods, and Physics-Informed Neural Networks (PINN) to simulate the blood glucose-insulin regulation mechanism in healthy individuals and diabetes patients via the Oral Glucose Tolerance Test (OGTT). It compares the performance of Runge-Kutta methods (RK4, adaptive RK45) and PINN in terms of accuracy, speed, and generalization ability.

Physiological Process of Blood Glucose Regulation

In the Oral Glucose Tolerance Test (OGTT), after blood glucose rises in healthy individuals, the pancreas secretes insulin, and blood glucose returns to normal within a few hours; diabetes patients have a malfunctioning regulation loop.

Importance of Modeling

Since the 1980s, OGTT has been a diagnostic standard for diabetes. Mathematical modeling can quantify pancreatic function, distinguish diabetes types, and design personalized insulin regimens.

Core Model: Randall's Dual ODE System

Uses a dual-coupled nonlinear ordinary differential equation (ODE) system to capture physiological processes:

• Blood glucose dynamic equation: Considers glucose input, insulin action, renal clearance, etc.
• Insulin dynamic equation: Pancreatic secretion mechanism in response to blood glucose. Key parameter B_b (pancreatic sensitivity): A low value corresponds to Type 1 diabetes, while a high value may lead to hypoglycemia.

The project implements three solution methods for comparison:

1. Classical Runge-Kutta 4th Order (RK4)

Fixed step size, fourth-order accuracy, simple implementation, low computational cost, implemented from scratch without external library dependencies.

2. Adaptive RK45

Dynamically adjusts step size (uses small steps in regions where the solution changes drastically, large steps in平缓 regions) to maintain accuracy while reducing the number of integration steps.

3. Physics-Informed Neural Network (PINN)

Embeds physical laws into neural network training. The loss function consists of data fidelity loss plus physical residual loss (penalizes prediction errors and violations of ODE constraints) to improve generalization ability.

Experimental Scenarios

1. Normal pancreatic function (baseline healthy state)
2. Normal pancreas + glucose infusion (simulate external intervention)
3. Reduced sensitivity (simulate Type 1 diabetes)
4. Increased sensitivity (simulate hypoglycemia)

Evaluation Metrics

• Accuracy: RMSE and MAE compared to the fine-step RK4 reference solution
• Speed: CPU wall-clock time
• Generalization Ability: Stability of PINN for unseen initial conditions

Performance of Classical Numerical Methods

• RK4: High accuracy at predictable cost; error decreases monotonically with step size reduction; good stability
• Adaptive RK45: Significantly reduces integration steps at similar accuracy, higher efficiency

Advantages of PINN

Successfully learns blood glucose-insulin dynamics and satisfies ODE constraints; physics-informed training improves generalization ability, suitable for sparse clinical data scenarios

Method Comparison Table

Dimension	Classical Solver	PINN
Computational Speed	Faster	Slower (requires training)
Flexibility	Fixed ODE form	Extensible to complex constraints
Generalization Ability	Single-solution	Fast inference after learning
Interpretability	High (explicit algorithm)	Medium (black box but with physical constraints)

Tech Stack

• R: Reproduce results from Chapter 2 of the original Schiesser work (deSolve package)
• Python: Implement RK4 and adaptive solvers from scratch (scipy.integrate) and benchmark tests
• PyTorch: Build PINN architecture, compute physical residuals via automatic differentiation
• LaTeX/Overleaf: IEEE conference report template
• GitHub Pages: Online documentation

Project Structure

• /ode_model/: Randall's dual ODE model definition + R reproduction
• /numerical_methods/: RK4 implementation from scratch + adaptive scheme
• /ml_dl/: PINN architecture, loss function, training and evaluation
• /results/: CSV outputs, benchmark tables, visualization charts

Clinical Value

The minimal dual ODE model can capture core physiology; classical solvers and PINN each have accuracy-speed trade-offs, providing references for diabetes management.

Application Scenarios

• Classical solvers: Suitable for real-time clinical monitoring (high-speed immediate feedback)
• PINN: Extensible to complex constraints (personalized parameters, multi-scale effects)

Future Directions

With the popularization of wearable devices and continuous glucose monitoring technology, such computational method comparisons will help develop the next generation of diabetes management tools.