abelsr1710/navier-stokes-2d-fno

Navier-Stokes 2D (ν = 1e-3)

Simulations of the 2D Navier-Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus, following the Fourier Neural Operator (FNO) benchmark of Li et al. (2021).

Each sample is the time evolution of the vorticity field w(x, y, t) on a periodic 64 × 64 grid over 20 time steps.

Intended use: this dataset is meant to be used for both training and testing / evaluation of neural operators and PDE surrogate models. It is shipped as a single pool of 1200 trajectories; you are expected to split it into train / validation / test subsets yourself (see Suggested splits below).

Summary

Property	Value
Number of samples (N)	1200
Spatial resolution	64 × 64
Time steps (T)	20
Viscosity (ν)	1e-3
Variable	Vorticity w(x, y, t)
dtype	float32
Tensor shape	[1200, 64, 64, 20] = [N, X, Y, T]
Domain	Unit torus [0, 1]² with periodic boundary conditions
Equation	2D incompressible Navier-Stokes (vorticity form)
Total size	~376 MB (.pt) / ~418 MB (Parquet)

Dataset structure

• Field: vorticity w(x, y, t), the scalar curl of the velocity field.
• Axes: [N, X, Y, T] — sample index, x-grid, y-grid, time.
• Grid: uniform 64 × 64, periodic on both spatial axes.
• Time: 20 snapshots per trajectory.
• No labels: this is an unsupervised / self-supervised spatiotemporal dataset; the "target" is defined by the forecasting task you set up (e.g. predict future steps from past steps).

Available formats

The dataset is published in two formats:

1. Parquet (data/) — directly loadable with the datasets library.
2. Original PyTorch tensor (navier_stokes_v1e-3_N1200_T20.pt) — the unmodified .pt.

Option A — datasets (Parquet)

from datasets import load_dataset

ds = load_dataset("abelsr1710/navier-stokes-2d-fno", split="train")
print(ds)
# Dataset({ features: ['vorticity'], num_rows: 1200 })

# One sample: nested list -> tensor [64, 64, 20]
import torch
w = torch.tensor(ds[0]["vorticity"])
print(w.shape)  # torch.Size([64, 64, 20])

Work with everything as a single PyTorch tensor:

ds.set_format("torch", columns=["vorticity"])
W = ds["vorticity"]          # [1200, 64, 64, 20]

Option B — Original PyTorch tensor (.pt)

import torch
from huggingface_hub import hf_hub_download

path = hf_hub_download(
    "abelsr1710/navier-stokes-2d-fno",
    "navier_stokes_v1e-3_N1200_T20.pt",
    repo_type="dataset",
)
W = torch.load(path, map_location="cpu")   # [1200, 64, 64, 20] float32

Suggested splits

Since the dataset is a single pool used for both training and evaluation, a common split is:

import torch
W = torch.load(path, map_location="cpu")   # [1200, 64, 64, 20]

n_train, n_test = 1000, 200
train, test = W[:n_train], W[n_train:n_train + n_test]

Typical usage (FNO)

To train a neural operator that maps past states to future states, a common recipe uses the first T_in steps as input and predicts the remaining steps:

T_in, T_out = 10, 10
x = W[..., :T_in]    # [N, 64, 64, 10]  -> model input
y = W[..., T_in:]    # [N, 64, 64, 10]  -> model target

Source & generation

These trajectories follow the data-generation setup of the original FNO work: a 2D incompressible Navier-Stokes solver in vorticity form on a periodic domain, with viscosity ν = 1e-3, random initial conditions, and a fixed forcing term. Snapshots are recorded over 20 time steps on a 64 × 64 grid. See the reference below for the full formulation.

Citation

If you use this dataset, please cite the original FNO work:

@inproceedings{li2021fourier,
  title={Fourier Neural Operator for Parametric Partial Differential Equations},
  author={Li, Zongyi and Kovachki, Nikola and Azizzadenesheli, Kamyar and
          Liu, Burigede and Bhattacharya, Kaushik and Stuart, Andrew and Anandkumar, Anima},
  booktitle={International Conference on Learning Representations (ICLR)},
  year={2021}
}

License

MIT.