Physics-Based AI modes for accelerating and increasing the Efficiency of CFD Simulations for Silicon Single Crystal Growth

A modular framework implementing variants of Physics-Informed Neural Networks (PINNs) for thermal-fluid coupling which includes Navier-Stokes equations CFD for crystal growth simulations.

Features

• Modular Design: Easily extendable framework for PINNs with clean separation of concerns
• Gradient Normalization: Improved training stability using advanced gradient normalization techniques
• Multiple PDE Support:
  • Navier-Stokes Equations for Crystal Growth (2D)
  • Navier-Stokes Equations for Crystal Growth (3D)
• **Neural Network **:
  • Physics-Inspired NNs
  • PI-GANO (GEOMETRY AWARE)
  • GAOT
• Visualization Tools: Comprehensive plotting utilities for solution visualization

Requirements

• Python 3.8+
• PyTorch 1.9+
• NumPy
• Matplotlib
• SciPy
• scikit-learn

Installation

# Clone the repository
git clone repo url
cd dir/

# Create a virtual environment (optional but recommended)
python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

# Install dependencies
pip install -r requirements.txt

Usage

The framework can be used through the command line interface:

python main.py --equation

Command Line Arguments

• --equation: Type of equation to solve (heat, schrodinger, kdv, crystal)
• --use_gn: Use gradient normalization for improved training
• --network_type: Neural network type (mlp or siren)
• --hidden_layers: Number of hidden layers in the neural network
• --neurons: Number of neurons per hidden layer
• --learning_rate: Learning rate for optimization
• --epochs: Number of training epochs
• --device: Device to use (cpu or cuda)
• --output_dir: Directory to save results

For Navier-Stokes crystal growth simulation:

• --viscosity: Kinematic viscosity coefficient
• --thermal_diffusivity: Thermal diffusivity
• --density: Fluid density
• --plot_resolution: Resolution for visualization plots

Examples

Crystal Growth Simulation using Navier-Stokes

python main.py --equation crystal --use_gn --network_type siren --hidden_layers 5 --neurons 100 --viscosity 0.01 --thermal_diffusivity 0.005 --epochs 5000

Future Work

• Add support for higher-dimensional and Thermal Coupling Equations
• Add more visualization options
• Extend crystal growth modeling capabilities
• Implement 3D Navier-Stokes equations

Acknowledgments

• Based on the PINN framework developed by Raissi et al.
• Gradient normalization techniques inspired by Wang et al.
• SIREN implementation based on the paper by Sitzmann et al.

Crystal Growth Simulation

This project simulates crystal growth using the Navier-Stokes, thermal coupling, and variants of Physics-Informed Geometry Aware AI models

Visualisation

To generate a series of frames showing the crystal growth:

python examples/simple_animation.py --frames 50

Options:

• --frames: Number of frames to generate (default: 50)
• --output-dir: Custom directory to save frames (optional)

After running the script, the frames will be saved in results/simple_animation/frames/ and an HTML slideshow will be created at results/simple_animation/slideshow.html.

Options:

• --frames: Number of frames in the video
• --duration: Duration of the video in seconds
• --fps: Frames per second
• --model: Path to saved model (optional)
• --train: Force training a new model

File Structure

• equations/: Contains the physical equations including Navier-Stokes
• models/: Neural network architectures (MLP, SIREN, GNPINN)
• utils/: Utility functions for training and visualization
• examples/: Example scripts
  • simple_animation.py: Creates frame-by-frame animation
  • crystal_growth_video.py: Full PINN-based simulation

The simulation creates both individual frames and an HTML slideshow for viewing the results. Open the slideshow in a web browser to see the animation with playback controls

License

This project is licensed under the MIT License - see the LICENSE file for details.