metadata
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configs:
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data_files:
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path: data/train-*
- config_name: finite_beta_1pct
data_files:
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path: finite_beta_1pct/train-*
- config_name: finite_beta_2pct
data_files:
- split: train
path: finite_beta_2pct/train-*
- config_name: finite_beta_3pct
data_files:
- split: train
path: finite_beta_3pct/train-*
- config_name: finite_beta_4pct
data_files:
- split: train
path: finite_beta_4pct/train-*
- config_name: finite_beta_5pct
data_files:
- split: train
path: finite_beta_5pct/train-*
- config_name: vmecpp_wout
data_files:
- split: train
path: vmecpp_wout/part*
- config_name: vmecpp_wout_finite_beta_1pct
data_files:
- split: train
path: vmecpp_wout_finite_beta_1pct/part*
- config_name: vmecpp_wout_finite_beta_2pct
data_files:
- split: train
path: vmecpp_wout_finite_beta_2pct/part*
- config_name: vmecpp_wout_finite_beta_3pct
data_files:
- split: train
path: vmecpp_wout_finite_beta_3pct/part*
- config_name: vmecpp_wout_finite_beta_4pct
data_files:
- split: train
path: vmecpp_wout_finite_beta_4pct/part*
- config_name: vmecpp_wout_finite_beta_5pct
data_files:
- split: train
path: vmecpp_wout_finite_beta_5pct/part*
license: mit
language:
- en
tags:
- physics
- fusion
- optimization
- neurips
pretty_name: ConStellaration
size_categories:
- 100K<n<1M
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.
The performance metrics and ideal MHD equilibria were evaluated under vacuum (default) and with plasma inside (finite beta).
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: https://arxiv.org/abs/2506.19583
- Code: https://github.com/proximafusion/constellaration
Dataset Structure
There are 6 tuples of datasets, one for each percentage of volume-averaged plasma inside the boundary:
| Condition | Boundaries, Metrics, Generation Settings, Misc | Ideal MHD Equilibira |
|---|---|---|
| Vacuum | default | vmecpp_wout |
| 1% Beta | finte_beta_1pct | vmecpp_wout_finite_beta_1pct |
| 2% Beta | finte_beta_2pct | vmecpp_wout_finite_beta_2pct |
| 3% Beta | finte_beta_3pct | vmecpp_wout_finite_beta_3pct |
| 4% Beta | finte_beta_4pct | vmecpp_wout_finite_beta_4pct |
| 5% Beta | finte_beta_5pct | vmecpp_wout_finite_beta_5pct |
Contents of datasets:
| default | vmecpp_wout |
|---|---|
Contains information about:
|
Contains:
|
| The default (vacuum) subset above is special in the sense that it contains more information than the other subsets (finite betas) below. Those are derived from the default (vacuum) subset by setting for each plasma boundary the respective volume-averaged beta percentage and re-computing the performance metrics and ideal MHD equilibria: | |
| finite_beta_*pct | vmecpp_wout_finite_beta_*pct |
Contains information about:
|
Same as vmecpp_wout above, corresponding to finite_beta_*pct |
For each of the components above there is an identifier column (ending with .id), a JSON column containing a JSON-string representation, as well as 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 pprint import pprint
ds = datasets.load_dataset(
"proxima-fusion/constellaration",
split="train",
num_proc=4,
)
ds = ds.select_columns([c for c in ds.column_names
if c.startswith("boundary.")
or c.startswith("metrics.")])
ds = ds.filter(
lambda x: x == 3,
input_columns=["boundary.n_field_periods"],
num_proc=4,
)
ml_ds = ds.remove_columns([
"boundary.n_field_periods", "boundary.is_stellarator_symmetric", # all same value
"boundary.r_sin", "boundary.z_cos", # empty
"boundary.json", "metrics.json", "metrics.id", # not needed
])
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
torch_ds = ml_ds.with_format("torch", device=device) # other options: "jax", "tensorflow" etc.
for batch in torch.utils.data.DataLoader(torch_ds, batch_size=4, num_workers=4):
pprint(batch)
break
Output
{'boundary.r_cos': tensor([[[ 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]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 9.9909e-01,
-6.8512e-02, -8.1567e-02, 2.5140e-02, -2.4035e-03],
[-3.4328e-03, 1.6768e-02, 1.2305e-02, -3.6708e-02, 1.0285e-01,
1.1224e-02, -2.3418e-02, -5.4137e-04, 9.3986e-04],
[-2.8389e-03, 1.4652e-03, 1.0112e-03, 9.8102e-04, -2.3162e-02,
-6.1180e-03, 1.5327e-03, 9.4122e-04, -1.2781e-03],
[ 3.9240e-04, -2.3131e-04, 4.5690e-04, -3.8244e-03, -1.5314e-03,
1.8863e-03, 1.1882e-03, -5.2338e-04, 2.6766e-04],
[-2.8441e-04, -3.4162e-04, 5.4013e-05, 7.4252e-04, 4.9895e-04,
-6.1110e-04, -8.7185e-04, -1.1714e-04, 9.9285e-08]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 1.0000e+00,
6.9176e-02, -1.8489e-02, -6.5094e-03, -7.6238e-04],
[ 1.4062e-03, 4.2645e-03, -1.0647e-02, -8.1579e-02, 1.0522e-01,
1.6914e-02, 6.5321e-04, 6.9397e-04, 2.0881e-04],
[-6.5155e-05, -1.2232e-03, -3.3660e-03, 9.8742e-03, -1.4611e-02,
6.0985e-03, 9.5693e-04, -1.0049e-04, 5.4173e-05],
[-4.3969e-04, -5.1155e-04, 6.9611e-03, -2.8698e-04, -5.8589e-03,
-5.4844e-05, -7.3797e-04, -5.4401e-06, -3.3698e-05],
[-1.9741e-04, 1.0003e-04, -2.0176e-04, 4.9546e-04, -1.6201e-04,
-1.9169e-04, -3.9886e-04, 3.3773e-05, -3.5972e-05]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 1.0000e+00,
1.1652e-01, -1.5593e-02, -1.0215e-02, -1.8656e-03],
[ 3.1697e-03, 2.1618e-02, 2.7072e-02, -2.4032e-02, 8.6125e-02,
-7.1168e-04, -1.2433e-02, -2.0902e-03, 1.5868e-04],
[-2.3877e-04, -4.9871e-03, -2.4145e-02, -2.1623e-02, -3.1477e-02,
-8.3460e-03, -8.8675e-04, -5.3290e-04, -2.2784e-04],
[-1.0006e-03, 2.1055e-05, -1.7186e-03, -5.2886e-03, 4.5186e-03,
-1.1530e-03, 6.2732e-05, 1.4212e-04, 4.3367e-05],
[ 7.8993e-05, -3.9503e-04, 1.5458e-03, -4.9707e-04, -3.9470e-04,
6.0808e-04, -3.6447e-04, 1.2936e-04, 6.3461e-07]]]),
'boundary.z_sin': tensor([[[ 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]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-8.5341e-02, 2.4825e-02, 8.0996e-03, -7.1501e-03],
[-1.3470e-03, 4.6367e-03, 4.1579e-02, -3.6802e-02, -1.5076e-01,
7.1852e-02, -1.9793e-02, 8.2575e-03, -3.8958e-03],
[-2.3956e-03, -5.7497e-03, 5.8264e-03, 9.4471e-03, -3.5171e-03,
-1.0481e-02, -3.2885e-03, 4.0624e-03, 4.3130e-04],
[ 6.3403e-05, -9.2162e-04, -2.4765e-03, 5.4090e-04, 1.9999e-03,
-1.1500e-03, 2.7581e-03, -5.7271e-04, 3.0363e-04],
[ 4.6278e-04, 4.3696e-04, 8.0524e-05, -2.4660e-04, -2.3747e-04,
5.5060e-05, -1.3221e-04, -5.4823e-05, 1.6025e-04]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-1.6090e-01, -1.4364e-02, 3.7923e-03, 1.8234e-03],
[ 1.2118e-03, 3.1261e-03, 3.2037e-03, -5.7482e-02, -1.5461e-01,
-1.8058e-03, -5.7149e-03, -7.4521e-04, 2.9463e-04],
[ 8.7049e-04, -3.2717e-04, -1.0188e-02, 1.1215e-02, -7.4697e-03,
-1.3592e-03, -1.4984e-03, -3.1362e-04, 1.5780e-06],
[ 1.2617e-04, -1.2257e-04, -6.9928e-04, 8.7431e-04, -2.5848e-03,
1.2087e-03, -2.4723e-04, -1.6535e-05, -6.4372e-05],
[-4.3932e-04, -1.8130e-04, 7.4368e-04, -6.1396e-04, -4.1518e-04,
4.8132e-04, 1.6036e-04, 5.3081e-05, 1.6636e-05]],
[[ 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
-1.1264e-02, -1.8349e-03, 7.2464e-03, 2.3807e-03],
[ 3.2969e-03, 1.9590e-02, 2.8355e-02, -1.0493e-02, -1.3216e-01,
1.7804e-02, 7.9768e-03, 2.1362e-03, -6.9118e-04],
[-5.2572e-04, -4.1409e-03, -3.6560e-02, 2.1644e-02, 1.6418e-02,
9.3557e-03, 3.3846e-03, 7.4172e-05, 1.8406e-04],
[-1.4907e-03, 2.0496e-03, -4.8581e-03, 3.5471e-03, -2.9191e-03,
-1.5056e-03, 7.7168e-04, -2.3136e-04, -1.2064e-05],
[-2.3742e-04, 4.5083e-04, -1.2933e-03, -4.4028e-04, 6.4168e-04,
-8.2755e-04, 4.1233e-04, -1.1037e-04, -6.3762e-06]]]),
'metrics.aspect_ratio': tensor([9.6474, 9.1036, 9.4119, 9.5872]),
'metrics.aspect_ratio_over_edge_rotational_transform': tensor([ 9.3211, 106.7966, 13.8752, 8.9834]),
'metrics.average_triangularity': tensor([-0.6456, -0.5325, -0.6086, -0.6531]),
'metrics.axis_magnetic_mirror_ratio': tensor([0.2823, 0.4224, 0.2821, 0.2213]),
'metrics.axis_rotational_transform_over_n_field_periods': tensor([0.2333, 0.0818, 0.1887, 0.1509]),
'metrics.edge_magnetic_mirror_ratio': tensor([0.4869, 0.5507, 0.3029, 0.2991]),
'metrics.edge_rotational_transform_over_n_field_periods': tensor([0.3450, 0.0284, 0.2261, 0.3557]),
'metrics.flux_compression_in_regions_of_bad_curvature': tensor([1.4084, 0.9789, 1.5391, 1.1138]),
'metrics.max_elongation': tensor([6.7565, 6.9036, 5.6105, 5.8703]),
'metrics.minimum_normalized_magnetic_gradient_scale_length': tensor([5.9777, 4.2971, 8.5928, 4.8531]),
'metrics.qi': tensor([0.0148, 0.0157, 0.0016, 0.0248]),
'metrics.vacuum_well': tensor([-0.2297, -0.1146, -0.0983, -0.1738])}
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:
from constellaration.geometry import surface_rz_fourier
ds = datasets.load_dataset(
"proxima-fusion/constellaration",
columns=["plasma_config_id", "boundary.json"],
split="train",
num_proc=4,
)
pandas_ds = ds.to_pandas().set_index("plasma_config_id")
plasma_config_id = "DQ4abEQAQjFPGp9nPQN9Vjf"
boundary_json = pandas_ds.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:
from constellaration.mhd import vmec_utils
wout_ds = datasets.load_dataset(
"proxima-fusion/constellaration",
"vmecpp_wout",
split="train",
streaming=True,
)
row = next(wout_ds.__iter__())
vmecpp_wout_json = row["json"]
vmecpp_wout = vmec_utils.VmecppWOut.model_validate_json(vmecpp_wout_json)
# Fetch corresponding boundary
plasma_config_id = row["plasma_config_id"]
boundary_json = pandas_ds.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"))
Match the boundaries from the default dataset to the corresponding metrics under a certain plasma condition:
import datasets
# Load default dataset to get the boundaries
default_ds = datasets.load_dataset(
"proxima-fusion/constellaration",
split="train",
num_proc=4,
)
# Load finite beta 3% dataset
finite_beta_3pct_ds = datasets.load_dataset(
"proxima-fusion/constellaration",
name="finite_beta_3pct",
split="train",
num_proc=4,
)
# Join the two datasets on plasma_config_id <-> misc.source_plasma_config_id
default_df = (
default_ds
.to_pandas()
.set_index("plasma_config_id")
.filter(like="boundary.")
)
finite_beta_3pct_df = (
finite_beta_3pct_ds
.to_pandas()
.set_index("misc.source_plasma_config_id")
)
finite_beta_3pct_with_boundaries_df = (
finite_beta_3pct_df
.join(default_df, how="inner") # joins on index
.reset_index(names="misc.source_plasma_config_id")
)
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{cadena2025constellaration,
title={ConStellaration: A dataset of QI-like stellarator plasma boundaries and optimization benchmarks},
author={Cadena, Santiago A and Merlo, Andrea and Laude, Emanuel and Bauer, Alexander and Agrawal, Atul and Pascu, Maria and Savtchouk, Marija and Guiraud, Enrico and Bonauer, Lukas and Hudson, Stuart and others},
journal={arXiv preprint arXiv:2506.19583},
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