Factorized Fourier Neural Operators

This repository contains the code to reproduce the results in our NeurIPS 2021 ML4PS workshop paper, Factorized Fourier Neural Operators.

The Fourier Neural Operator (FNO) is a learning-based method for efficiently simulating partial differential equations. We propose the Factorized Fourier Neural Operator (F-FNO) that allows much better generalization with deeper networks. With a careful combination of the Fourier factorization, weight sharing, the Markov property, and residual connections, F-FNOs achieve a six-fold reduction in error on the most turbulent setting of the Navier-Stokes benchmark dataset. We show that our model maintains an error rate of 2% while still running an order of magnitude faster than a numerical solver, even when the problem setting is extended to include additional contexts such as viscosity and time-varying forces. This enables the same pretrained neural network to model vastly different conditions.

Getting Started

# Set up pyenv and pin python version to 3.9.7
curl https://pyenv.run | bash
# Configure our shell's environment for pyenv
pyenv install 3.9.7
pyenv local 3.9.7

# Set up poetry
curl -sSL https://raw.githubusercontent.com/python-poetry/poetry/master/install-poetry.py | python -
export PATH="$HOME/.local/bin:$PATH"

# Install all python dependencies
poetry install
source .venv/bin/activate # or: poetry shell
# If we need to use Jupyter notebooks
python -m ipykernel install --user --name fourierflow --display-name "fourierflow"
# Temp fix until allennlp has upgraded transformers dependencies to 4.11
poe update-transformers
# Manually reinstall Pytorch with CUDA 11.1 support
# Monitor poetry's support for pytorch here: https://github.com/python-poetry/poetry/issues/2613
poe install-torch-cuda11

# set default paths
cp example.env .env
# The environment variables in .env will be loaded automatically when running
# fourierflow train, but we can also load them manually in our terminal
export $(cat .env | xargs)

# Alternatively, you can pass the paths to the system using env vars, e.g.
FNO_DATA_ROOT=/My/Data/Location fourierflow

Navier Stokes Experiments

You can download all of our datasets and pretrained model as follows:

# Datasets (209GB)
wget --continue https://object-store.rc.nectar.org.au/v1/AUTH_c0e4d64401cf433fb0260d211c3f23f8/fourierflow/data.tar.gz
tar -zxvf data.tar.gz

# Pretrained models and results (30GB)
wget --continue https://object-store.rc.nectar.org.au/v1/AUTH_c0e4d64401cf433fb0260d211c3f23f8/fourierflow/experiments.tar.gz
tar -zxvf experiments.tar.gz

Alternatively, you can also generate the datasets from scratch:

# Download Navier Stokes datasets
fourierflow download fno

# Generate Navier Stokes on toruses with a different forcing function and
# viscosity for each sample. Takes 14 hours.
fourierflow generate navier-stokes --force random --cycles 2 --mu-min 1e-5 \
    --mu-max 1e-4 --steps 200 --delta 1e-4 \
    data/navier-stokes/random_force_mu.h5

# Generate Navier Stokes on toruses with a different time-varying forcing
# function and a different viscosity for each sample. Takes 21 hours.
fourierflow generate navier-stokes --force random --cycles 2 --mu-min 1e-5 \
    --mu-max 1e-4 --steps 200 --delta 1e-4 --varying-force \
    data/navier-stokes/random_varying_force_mu.h5

# If we decrease delta from 1e-4 to 1e-5, generating the same dataset would now
# take 10 times as long, while the difference between the solutions in step 20
# is only 0.04%.

Training and test commands:

# Reproducing SOA model on Navier Stokes from Li et al (2021).
fourierflow train --trial 0 experiments/navier_stokes_4/zongyi/4_layers/config.yaml

# Train with our best model
fourierflow train --trial 0 experiments/navier_stokes_4/markov/24_layers/config.yaml

# Get inference time on test set
fourierflow predict --trial 0 experiments/navier_stokes_4/markov/24_layers/config.yaml

Visualization commands:

# Create all plots and tables for paper
fourierflow plot layer
fourierflow plot complexity
fourierflow plot table-3

# Create the flow animation for presentation
fourierflow plot flow

# Create plots for the poster
fourierflow plot poster

Experiments with Fourier layers on simulation data.

Related tags

Overview

Factorized Fourier Neural Operators

Getting Started

Navier Stokes Experiments

Owner

Alasdair Tran

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