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configs:
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data_files:
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path: data/train-*
- config_name: full_flat
data_files:
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path: full_flat/train-*
- config_name: full_json
data_files:
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path: vmecpp_ideal_mhd_equilibria/part-*
license: mit
language:
- en
tags:
- physics
- fusion
- optimization
- neurips
pretty_name: ConStellaration
size_categories:
- 10K<n<100K
Dataset Card for ConStellaration
A dataset of diverse quasi-isodynamic (QI) stellarator boundary shapes with corresponding performance metrics and ideal magneto-hydrodynamic (MHD) equilibria, as well as settings for their generation.
Dataset Details
Dataset Description
Stellarators are magnetic confinement devices that are being pursued to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Specifically, QI-stellarators are seen as a promising path to commercial fusion due to their intrinsic avoidance of current-driven disruptions. With the release of this dataset, we aim to lower the barrier for optimization and machine learning researchers to contribute to stellarator design, and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.
- Curated by: Proxima Fusion
- License: MIT
Dataset Sources
- Repository: https://huggingface.co/datasets/proxima-fusion/constellaration
- Paper: [not published yet]
- Code: https://github.com/proximafusion/constellaration
Dataset Structure
The dataset consists of 2 tabular parts. Both parts have a column plasma_config_id in common which can be used to associate respective entries:
| full_json/full_flat | vmecpp_ideal_mhd_equilibria |
|---|---|
Contains information about:
|
Contains, for each plasma boundary, a JSON representations of the "WOut" file as obtained when running VMEC, initialized on the boundary. The JSON representation can be converted to a VMEC2000 output file. |
The full_json variant of the dataset contains for each of the components listed about an identifier column (ending with .id), as well as a JSON column.
The full_flat variant contains the same information as full_json but with all JSON columns flattened into one column per leaf in the nested JSON structure (with . separating the keys on the JSON path to the respective leaf).
Uses
Install Huggingface Datasets: pip install datasets
Basic Usage
Load the dataset and convert to a Pandas Dataframe (here, torch is used as an example; install it with" pip install torch):
import datasets
import torch
from torch.utils.data import DataLoader
full_flat_ds = datasets.load_dataset("proxima-fusion/constellaration", "full_flat")["train"]
full_flat_ds = full_flat_ds.select_columns([c for c in full_flat_ds.column_names
if c.startswith("boundary.")
or c.startswith("metrics.")])
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
ds_torch = full_flat_ds.with_format("torch", device=device) # other options: "jax", "tensorflow" etc.
for batch in DataLoader(ds_torch, batch_size=4, num_workers=4):
print(batch)
break
Output
{'metrics.id': ['DfpsEPzxXHTUgveVPNFVxyw',
'D6ydRp85utx9ZXqZVXbez8G',
'DLfSjAoEr26nCNet4S84XET',
'DBVNupAx3tW54uUz5bGQfyT'],
'metrics.qi': tensor([0.0101, 0.0007, 0.0249, 0.0148]),
'metrics.vacuum_well': tensor([-0.0216, -0.0756, -0.1321, -0.2297]),
'metrics.aspect_ratio': tensor([7.7955, 8.7009, 8.3073, 9.6474]),
'metrics.max_elongation': tensor([7.9947, 5.7292, 5.6427, 6.7565]),
'metrics.average_triangularity': tensor([ 0.6554, -0.6067, -0.3194, -0.5184]),
'metrics.axis_magnetic_mirror_ratio': tensor([0.2098, 0.2465, 0.5243, 0.2823]),
'metrics.edge_magnetic_mirror_ratio': tensor([0.3518, 0.2744, 0.7742, 0.4869]),
'metrics.aspect_ratio_over_edge_rotational_transform': tensor([ 4.7622, 39.3853, 7.4686, 9.3211]),
'metrics.flux_compression_in_regions_of_bad_curvature': tensor([2.0642, 1.6771, 1.6702, 1.4084]),
'metrics.axis_rotational_transform_over_n_field_periods': tensor([0.3285, 0.2195, 0.2377, 0.2333]),
'metrics.edge_rotational_transform_over_n_field_periods': tensor([0.3274, 0.1105, 0.2225, 0.3450]),
'metrics.minimum_normalized_magnetic_gradient_scale_length': tensor([5.0333, 4.4903, 2.7130, 5.9777]),
'boundary.r_cos': tensor([[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 9.9949e-01,
7.6796e-04, -1.6605e-02, 5.5780e-04, 2.7140e-06],
[ 9.0751e-04, -3.6262e-03, -2.5385e-02, -7.7356e-02, 2.1363e-01,
-4.3046e-02, 7.0488e-03, -1.9437e-03, -1.4148e-04],
[ 1.1192e-03, 6.2549e-03, 2.5220e-02, 2.2216e-02, -1.7012e-02,
-1.9742e-03, 3.0245e-03, -8.5555e-04, 1.9455e-04],
[-1.0992e-03, -3.0390e-03, -1.9017e-03, -5.2155e-03, -5.7048e-03,
2.0575e-03, -1.1494e-04, 1.6793e-04, -4.5783e-05],
[ 2.3317e-04, -2.0280e-04, 4.0296e-04, 7.2199e-05, 1.3698e-04,
-7.0448e-05, 2.9516e-04, -9.0838e-05, -6.2693e-06]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 9.9334e-01,
9.5655e-02, -5.2197e-02, -9.8426e-03, -5.2107e-04],
[-6.9068e-04, -2.0027e-04, 1.4961e-03, -4.8040e-02, 1.5062e-01,
-8.6001e-04, 9.8727e-03, 1.3859e-03, -1.4257e-04],
[ 2.1268e-03, -5.4152e-03, -1.2367e-02, -1.8891e-02, -2.2634e-02,
2.4878e-03, 1.7472e-03, 1.7854e-04, 1.5837e-04],
[ 2.9863e-04, 1.3137e-03, -3.4623e-03, -5.5232e-03, -2.7664e-04,
2.9050e-03, 1.1163e-03, 3.4548e-04, 1.1368e-04],
[ 7.7059e-05, -2.3845e-04, 4.4021e-04, 1.2212e-04, -2.1361e-04,
-5.2118e-04, -1.5413e-04, -1.6513e-04, 1.4236e-06]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 1.0000e+00,
9.7826e-02, -3.5796e-02, 4.3583e-04, 4.1021e-04],
[ 1.8546e-03, 4.6983e-03, 3.2687e-02, 6.7351e-02, 6.6784e-02,
-4.2107e-02, 1.4765e-02, -1.3257e-03, -1.3003e-04],
[-9.6934e-04, -3.8986e-03, -1.0552e-02, -4.2583e-03, -8.3177e-03,
-6.7278e-05, 3.3263e-04, -1.0408e-03, 2.2868e-04],
[ 2.6668e-04, 6.7729e-04, 2.6165e-03, 1.2503e-03, -1.4094e-03,
9.9661e-04, -8.1563e-04, 4.4246e-04, -1.1460e-04],
[ 3.5259e-05, -1.1595e-04, -1.3741e-04, 5.9814e-05, -5.7761e-04,
3.7886e-04, -1.9925e-04, 6.7852e-05, -3.0395e-05]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 1.0000e+00,
-6.5763e-02, -3.8500e-02, 2.2178e-03, 4.6007e-04],
[-6.6648e-04, -1.0976e-02, 5.6475e-02, 1.4193e-02, 8.3476e-02,
-4.6767e-02, -1.3679e-02, 3.9562e-03, 1.0087e-04],
[-3.5474e-04, 4.7144e-03, 8.3967e-04, -1.9705e-02, -9.4592e-03,
-5.8859e-03, 1.0172e-03, 9.2020e-04, -2.0059e-04],
[ 2.9056e-03, 1.6125e-04, -4.0626e-04, -8.0189e-03, 1.3228e-03,
-5.3636e-04, -7.3536e-04, 3.4558e-05, 1.4845e-04],
[-1.2475e-04, -4.9942e-04, -2.6091e-04, -5.6161e-04, 8.3187e-05,
-1.2714e-04, -2.1174e-04, 4.1940e-06, -4.5643e-05]]]),
'boundary.z_sin': tensor([[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-1.9626e-01, 1.9675e-02, -2.2323e-03, 6.1945e-04],
[-5.1524e-04, -3.8208e-03, -3.4611e-02, -7.3697e-02, -9.4725e-02,
1.4401e-02, -4.8538e-03, 1.1153e-03, 1.8119e-04],
[ 8.8862e-04, 4.7645e-03, 1.4034e-02, -1.3992e-02, 1.4160e-02,
3.7312e-04, -7.9215e-04, -2.4587e-04, -4.4745e-05],
[-1.1121e-03, -5.1679e-03, -3.6563e-03, 1.3666e-02, 1.2211e-03,
-7.2069e-04, -6.1250e-04, 2.2509e-04, -5.6412e-05],
[ 1.5477e-04, 6.2145e-04, 3.0922e-04, 3.2419e-05, 2.4620e-04,
-6.8060e-04, 1.9615e-04, -5.1384e-05, 3.9863e-05]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-4.6604e-01, -4.8706e-02, -5.5774e-03, -2.5693e-03],
[-2.2537e-03, -3.5303e-04, 1.5423e-02, -7.8331e-02, -1.0906e-01,
6.5595e-02, 8.1187e-04, -1.4336e-03, 1.4737e-03],
[ 2.4240e-03, -1.4512e-03, 1.5746e-03, 1.0027e-02, -1.0979e-02,
-7.1742e-03, -3.0459e-03, -1.4641e-03, 1.1328e-04],
[ 1.3788e-03, 9.4350e-04, -8.9247e-03, 3.6596e-03, -5.4934e-04,
4.0136e-03, -2.9544e-04, 3.2837e-04, 1.0018e-04],
[ 2.9187e-04, 7.0291e-04, -2.3282e-03, -4.5468e-04, 1.0021e-03,
6.0775e-04, -3.5128e-04, 5.7630e-05, -1.2590e-04]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
6.2592e-02, 1.8552e-02, 1.7140e-03, 3.3028e-05],
[ 1.7765e-03, 1.2827e-02, 4.8849e-02, 6.8718e-03, -1.9011e-01,
7.3130e-02, -2.1610e-02, 3.1883e-03, -5.4797e-04],
[-1.7520e-03, -1.0653e-02, -1.6171e-02, 4.8786e-03, 5.1656e-03,
-3.2699e-03, 3.5506e-03, -6.1073e-05, -5.3629e-05],
[-2.1859e-04, -1.4518e-03, -2.4928e-03, -3.6855e-03, -1.1030e-04,
2.5252e-04, 4.9944e-04, -3.5102e-04, 5.2259e-05],
[ 9.7048e-05, -3.4866e-04, -6.1121e-05, 1.1803e-03, -4.2218e-04,
4.5423e-04, -2.6355e-04, 9.2855e-05, -4.8167e-06]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-1.4295e-02, 1.4929e-02, -6.6461e-03, -3.0652e-04],
[ 9.6958e-05, -1.6067e-03, 5.7568e-02, -2.2848e-02, -1.6101e-01,
1.6560e-02, 1.5032e-02, -1.2463e-03, -4.0128e-04],
[-9.9541e-04, 3.6108e-03, -1.1401e-02, -1.8894e-02, -7.7459e-04,
9.4527e-03, -4.6871e-04, -5.5180e-04, 3.2248e-04],
[ 2.3465e-03, -2.4885e-03, -8.4212e-03, 8.9649e-03, -1.9880e-03,
-1.6269e-03, 8.4700e-04, 3.7171e-04, -6.8400e-05],
[-3.6228e-04, -1.8575e-04, 6.0890e-04, 5.0270e-04, -6.9953e-04,
-7.6356e-05, 2.3796e-04, -3.2524e-05, 5.3396e-05]]]),
'boundary.r_sin': tensor([nan, nan, nan, nan]),
'boundary.z_cos': tensor([nan, nan, nan, nan]),
'boundary.n_field_periods': tensor([5., 2., 5., 3.]),
'boundary.is_stellarator_symmetric': tensor([True, True, True, True])}
Advanced Usage
For advanced manipulation and visualization of data contained in this dataset, install constellaration from here:
pip install constellaration
Load and instantiate plasma boundaries:
import datasets
from constellaration.geometry import surface_rz_fourier
full_json_ds = datasets.load_dataset("proxima-fusion/constellaration", "full_json")["train"]
full_json_df = full_json_ds.to_pandas().set_index("plasma_config_id")
plasma_config_id = "DQ4abEQAQjFPGp9nPQN9Vjf"
boundary_json = full_json_df.loc[plasma_config_id]["boundary.json"]
boundary = surface_rz_fourier.SurfaceRZFourier.model_validate_json(boundary_json)
Plot boundary:
from constellaration.utils import visualization
visualization.plot_surface(boundary).show()
visualization.plot_boundary(boundary).get_figure().show()
| Boundary | Cross-sections |
|---|---|
 |
 |
Stream and instantiate the VMEC ideal MHD equilibria:
import datasets
from constellaration.mhd import vmec_utils
from constellaration.geometry import surface_rz_fourier
vmec_wout_ds = datasets.load_dataset("proxima-fusion/constellaration", "vmecpp_ideal_mhd_equilibria", streaming=True)["train"]
vmec_wout_ds = vmec_wout_ds.filter(lambda row: row["vmecpp_wout_json"] is not None)
row = next(vmec_wout_ds.__iter__())
vmecpp_wout_json = row["vmecpp_wout_json"]
vmecpp_wout = vmec_utils.VmecppWOut.model_validate_json(vmecpp_wout_json)
# Fetch corresponding boundary
full_json_ds = datasets.load_dataset("proxima-fusion/constellaration", "full_json")["train"]
full_json_df = full_json_ds.to_pandas().set_index("plasma_config_id")
plasma_config_id = row["plasma_config_id"]
boundary_json = full_json_df.loc[plasma_config_id]["boundary.json"]
boundary = surface_rz_fourier.SurfaceRZFourier.model_validate_json(boundary_json)
Plot flux surfaces:
from constellaration.utils import visualization
visualization.plot_flux_surfaces(vmecpp_wout, boundary)
Save ideal MHD equilibrium to VMEC2000 WOut file:
import pathlib
from constellaration.utils import file_exporter
file_exporter.to_vmec2000_wout_file(vmecpp_wout, pathlib.Path("vmec2000_wout.nc"))
Dataset Creation
Curation Rationale
Wide-spread community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations.
Source Data
Data Collection and Processing
We generated this dataset by sampling diverse QI fields and optimizing stellarator plasma boundaries to target key properties, using four different methods.
Who are the source data producers?
Proxima Fusion's stellarator optimization team.
Personal and Sensitive Information
The dataset contains no personally identifiable information.
Citation
BibTeX:
@article{article_id, author = {Santiago A Cadena, Andrea Merlo, Emanuel Laude, Alexander Bauer, Atul Agrawal, Maria Pascu, Marija Savtchouk, Lukas Bonauer, Enrico Guiraud, Stuart R. Hudson, Markus Kaiser}, title = {ConStellaration: A dataset of QI-like stellarator plasma boundaries and optimization benchmarks}, journal = {NeurIPS 2025 Datasets and Benchmarks Track}, year = {2025} }
Glossary
| Abbreviation | Expansion |
|---|---|
| QI | Quasi-Isodynamic(ity) |
| MHD | Magneto-Hydrodynamic |
| DESC | Dynamical Equilibrium Solver for Confinement |
| VMEC/VMEC++ | Variational Moments Equilibrium Code (Fortran/C++) |
| QP | Quasi-Poloidal |
| NAE | Near-Axis Expansion |
| NFP | Number of Field Periods |
Dataset Card Authors
Alexander Bauer, Santiago A. Cadena