FNO (Fourier Neural Operator) Tutorial

Path

Stage 1: Theory (1-2 days)

• Li et al., "Fourier Neural Operator for Parametric PDEs", ICLR 2021
• Neural Operator learns the solution operator, not a finite-dimensional map

Stage 2: Code (3-5 days)

Official PyTorch implementation:

git clone https://github.com/neuraloperator/neuraloperator
cd neuraloperator

Learning order:

• scripts/train_darcy.py: Darcy flow data loading + training loop (best starting point)
• neuralop/models/: FNO implementation
• neuralop/layers/: spectral convolution (read torch.fft)
• reproduce on AirfRANS (airfoil RANS surrogate)

Stage 3: Advanced (1-2 weeks)

• Spectral bias and its fixes
• Time-FNO for time-dependent PDEs (NS)
• Ablation vs DeepONet / PINN

Practice projects

1. Darcy flow: smallest start, trains in 10 min
2. NACA airfoil: AirfRANS subset for FNO accuracy
3. U-bend: engineering-realistic, indexed here

Who it's for

• Engineers/researchers with PyTorch background
• Those wanting neural operators vs traditional PINN
• Anyone building CFD/CAE surrogates