pinns-medical-modeling - SKILL.md Agent Skill

name: pinns-medical-modeling description: "Physics-Informed Neural Networks (PINNs) for medical modeling and biomedical simulation. Solve differential equations governing physiological processes (cardiovascular, neural, pharmacokinetic) using neural networks that embed physical laws as constraints. Use when: (1) Modeling patient-specific physiology, (2) Solving inverse problems in biomechanics, (3) Drug pharmacokinetic modeling, (4) Cardiac or neural dynamics simulation with limited data."

PINNs Medical Modeling

Physics-Informed Neural Networks for medical and biomedical simulation.

Activation Keywords

PINNs medical
physics-informed neural network medical
biomedical simulation
physiological modeling neural network
medical differential equations
物理信息神经网络医学
生物医学仿真
cardiac PINNs
pharmacokinetic neural network

Tools Used

exec: Run Python PINNs training scripts (PyTorch/JAX)
read: Load physiological data, ODE/PDE specifications
write: Generate PINNs model code and simulation results

Core Workflow

Step 1: Define Physical Laws

Specify the governing equations (ODEs/PDEs) for the physiological system:

# Example: Hodgkin-Huxley neuron model
def physics_residual(t, V, m, h, n, params):
    """PDE residual for Hodgkin-Huxley equations."""
    C_m, g_Na, g_K, g_L = params
    dV_dt = (1/C_m) * (I_ext - g_Na*m**3*h*(V-E_Na) 
                        - g_K*n**4*(V-E_K) - g_L*(V-E_L))
    return dV_dt

Step 2: Design Neural Network

Create network to approximate solution, with physics loss added to data loss:

class PINNModel(nn.Module):
    def __init__(self):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(1, 64), nn.Tanh(),
            nn.Linear(64, 64), nn.Tanh(),
            nn.Linear(64, 1)
        )

    def forward(self, t):
        return self.net(t)

Step 3: Define Combined Loss

loss = data_loss + lambda_physics * physics_loss + lambda_bc * boundary_loss

Step 4: Train with Adaptive Sampling

Use collocation points in domain; add extra points near boundaries and discontinuities.

Instructions for Agents

Step 1: Identify Medical System

Determine physiological system: cardiovascular, neural, pharmacokinetic, or biomechanical.

Step 2: Extract Governing Equations

From the medical/physics paper, extract ODEs/PDEs that govern the system.

Step 3: Formulate PINN

Design neural network architecture; define physics residual loss; set boundary/initial conditions.

Step 4: Train and Validate

Train with combined data + physics loss; validate against clinical measurements or analytical solutions.

Step 5: Report

Report model accuracy, physics constraint satisfaction, and clinical relevance.

Examples

Example 1: Cardiac Electrophysiology Simulation

User: "Simulate cardiac action potential using PINNs"

Agent:
1. Extract governing equations: Hodgkin-Huxley or monodomain model
2. Design PINNs: input=time, output=membrane voltage
3. Define physics loss from action potential ODE
4. Train on sparse electrode measurements
5. Report simulated action potential vs clinical data

Example 2: Pharmacokinetic Modeling

User: "Model drug concentration over time with limited patient data"

Agent:
1. Extract PK model: two-compartment ODE system
2. Design PINNs to approximate concentration curves
3. Embed ODE constraints as physics loss
4. Train on available blood samples
5. Predict drug concentration with uncertainty estimates

Resources

references/: PINNs implementation guides and medical domain references
Related: neural-dynamics-decision-making, jedi-neural-dynamics-inference