2ailesB/enma-datasets

ENMA: Tokenwise Autoregression for Generative Neural PDE Operators

This repository provides the datasets used in the paper "ENMA: Tokenwise Autoregression for Generative Neural PDE Operators.", presented at NeurIPS 2025 as Spotlight.

Project Page | ArXiv | Code

Usage

To use these datasets with the provided code, follow the setup instructions from the official repository:

git clone https://github.com/armandkassai/ENMA.git
cd ENMA

conda create -n enma python=3.10 -y
conda activate enma
pip install -e .

PDEs

We provide 5 datasets:

• Combined equation (1d space + time)
• Advection equation (1d space + time)
• Gray-Scott equation (2d space + time)
• Wave equation (2d space + time)
• Vorticity (2d space + time)

Each dataset provides $12,00012,000$ trajectories for training and $1,2001,200$ for testing and validation. On top of that an _ood version with $120120$ trajectories is proposed for each of them.

Parameter ranges are summurized in the following table.

Dataset	Parameter	In-D	Out-D
Combined	$\alpha \backslash alpha$	$\mathcal{U}([0.3,0.5])\backslash mathcal\{U\}([0.3,\; 0.5])$	$\mathcal{U}([0.3,0.5])\backslash mathcal\{U\}([0.3,\; 0.5])$
	$\beta \backslash beta$	$\mathcal{U}([0.0005,0.5])\backslash mathcal\{U\}([0.0005,\; 0.5])$	$\mathcal{U}([0.0005,0.5])\backslash mathcal\{U\}([0.0005,\; 0.5])$
	$\gamma \backslash gamma$	$\mathcal{U}([0.01,1])\backslash mathcal\{U\}([0.01,\; 1])$	$\mathcal{U}([0.01,1])\backslash mathcal\{U\}([0.01,\; 1])$
	$\delta \backslash delta$	—	$\mathcal{U}([0.5,1])\backslash mathcal\{U\}([0.5,\; 1])$
Advection	$\alpha \backslash alpha$	$\mathcal{U}([-5,5])\backslash mathcal\{U\}([-5,\; 5])$	$\mathcal{U}([-7,-5]\cup [5,7])\backslash mathcal\{U\}([-7,\; -5]\; \backslash cup\; [5,\; 7])$
Wave	$cc$	$\mathcal{U}([100,500])\backslash mathcal\{U\}([100,\; 500])$	$\mathcal{U}([500,550])\backslash mathcal\{U\}([500,\; 550])$
	$kk$	$\mathcal{U}([0,50])\backslash mathcal\{U\}([0,\; 50])$	$\mathcal{U}([50,60])\backslash mathcal\{U\}([50,\; 60])$
Gray-Scott	$FF$	$\mathcal{U}([0.023,0.045])\backslash mathcal\{U\}([0.023,\; 0.045])$	$\mathcal{U}([0.045,0.0467])\backslash mathcal\{U\}([0.045,\; 0.0467])$
	$kk$	$\mathcal{U}([0.0590,0.0640])\backslash mathcal\{U\}([0.0590,\; 0.0640])$	$\mathcal{U}([0.0570,0.0590])\backslash mathcal\{U\}([0.0570,\; 0.0590])$
Vorticity	$\nu \backslash nu$	$\mathcal{U}([{10}^{-3},{10}^{-2}])\backslash mathcal\{U\}([10^\{-3\},\; 10^\{-2\}])$	$\mathcal{U}([{10}^{-5},{10}^{-4}])\backslash mathcal\{U\}([10^\{-5\},\; 10^\{-4\}])$

Please refer to the paper or code for additional details on the PDEs, parameter ranges, and Dataloaders for in- and out-of-distribution versions.

What's inside the datasets

Each dataset provides the PDE trajectory $uu$ along with the PDE parameters, forcing terms (if involved), initial conditions (if involved), and boundary conditions (if involved).

The PPDEGeneration Package that was used to generate the data also contains scripts for creating torch dataloader.

Citation

@inproceedings{
  koupai2025enma,
  title={{ENMA}: Tokenwise Autoregression for Continuous Neural {PDE} Operators},
  author={Armand Kassa{\"\i} Koupa{\"\i} and Lise Le Boudec and Louis Serrano and Patrick Gallinari},
  booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
  year={2025},
  url={https://openreview.net/forum?id=3CYXSMFv55}
  }