muTransfer-FNO Dataset

Benchmark datasets for Maximal Update Parametrization and Zero-Shot Hyperparameter Transfer for Fourier Neural Operators (ICML 2025).

Code: https://github.com/LithiumDA/muTransfer-FNO

Contains data for three PDE problems: Navier-Stokes, Burgers' equation, and Darcy Flow.

File Structure

├── ns/
│   ├── get_full_data.py        # Script to combine NS parts
│   ├── ns_part_01.npy          # Navier-Stokes samples 0–99
│   ├── ns_part_02.npy          # Navier-Stokes samples 100–199
│   └── ns_part_03.npy          # Navier-Stokes samples 200–299
├── burgers/
│   └── burgers_data_R10.mat    # Burgers' equation (R=10)
└── darcy/
    ├── piececonst_r421_N1024_smooth1.mat   # Darcy Flow dataset 1
    └── piececonst_r421_N1024_smooth2.mat   # Darcy Flow dataset 2

Datasets

Navier-Stokes (Re=500, T=300)

300 time steps of a high-resolution 3D Navier-Stokes simulation at Reynolds number 500. Split into three .npy files (NumPy binary format), each containing a contiguous slice along the time dimension.

Burgers' Equation

Burgers' equation dataset at resolution 8192 with viscosity 1e-1 (R=10). Stored as a MATLAB .mat file.

Darcy Flow

Darcy Flow equation datasets on a 421x421 grid with 1024 samples each. Two variants with different coefficient smoothness levels. Stored as MATLAB .mat files.

Usage

# Navier-Stokes
import numpy as np
ns_data = np.load("ns/ns_part_01.npy")

# Burgers / Darcy
import scipy.io
burgers = scipy.io.loadmat("burgers/burgers_data_R10.mat")
darcy = scipy.io.loadmat("darcy/piececonst_r421_N1024_smooth1.mat")

Citation

@inproceedings{li2025maximal,
  title={Maximal Update Parametrization and Zero-Shot Hyperparameter Transfer for Fourier Neural Operators},
  author={Li, Shanda and Maddox, Wesley J},
  booktitle={International Conference on Machine Learning (ICML)},
  year={2025}
}