Physics-Informed Neural Networks for Tokamak Plasma Evolution

This project demonstrates the application of Physics-Informed Neural Networks (PINNs) to predict the temporal evolution of plasma temperature profiles in tokamak fusion devices. The model combines data-driven learning with physical constraints from plasma transport equations.

Takeaway

Why does temperature profile mismatch with ground truth more in the first 5% of time?

• Look into the boundary condition (initial). Maybe the boudary condition is not defined aligning with the simulated/collected data. This could be resulting from the following issue of a boundary condition tha cannot generalise to new data.
• If you define/learn different boundary conditions every time you train the model with another set of data, the boundary condition is not generalisable and this affects the generalisability to drifted data distribution Other spots for quick check:
• In the loss function, is the PDE loss or boundary condition loss with too small a weight.

Overview

The project implements a PINN to learn and predict the spatio-temporal evolution of plasma temperature, constrained by the heat diffusion equation:

∂T(r,t)/∂t = D ∇²T(r,t) + S(r,t)

where:

• T(r,t) is the temperature profile
• r is the minor radius
• t is time
• D is thermal diffusivity
• S(r,t) represents heating/cooling sources

Project Structure

.
├── codes/
│   ├── PINN_Plasma_Evolution_Prediction.ipynb   # Main PINN implementation
│   ├── pinn_model.pth                          # Trained model weights
│   └── realistic_plasma_data.py                # Realistic data generation
├── figs_tabs/                                  # Generated figures and tables
├── models/                                     # Model checkpoints
└── README.md                                   # This file

Features

• Physics-informed neural network implementation in PyTorch
• Realistic plasma temperature profile generation including:
  • Core temperature peaking
  • Edge pedestal
  • Time-dependent heating and cooling phases
• Comparison with traditional Gaussian Process regression
• Visualization of predictions and PDE residuals

Requirements

• Python 3.7+
• PyTorch
• NumPy
• Matplotlib
• scikit-learn (for Gaussian Process comparison)

Usage

1. Open codes/PINN_Plasma_Evolution_Prediction.ipynb in Jupyter
2. Run all cells to:
   • Generate training data
   • Train the PINN model
   • Compare with Gaussian Process regression
   • Visualize results

Results

The model demonstrates:

• Accurate prediction of plasma temperature evolution
• Physics-consistent solutions (verified by PDE residuals)
• Comparison between physics-informed and pure data-driven approaches

Results are visualized in figs_tabs/ including PDE residual plots and prediction comparisons.

References

1. Raissi et al., "Physics-informed neural networks," J. Comput. Phys., 2019
2. Karniadakis et al., "Physics-informed machine learning," Nat. Rev. Phys., 2021
3. Seo et al., "Avoiding fusion plasma tearing instability with deep reinforcement learning," Nature, 2023