FNO (Fourier Neural Operator) Tutorial

License: MIT · Updated 2026-08-01
Official → Paper →

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
  • Learning order: datasets -> models/FNO.py -> train.py -> reproduce on AirfRANS

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
Tags: FNONeural OperatorSurrogateTutorialPyTorch