--- dataset_info: - config_name: default features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: boundary.json dtype: string - name: boundary.is_stellarator_symmetric dtype: bool - name: boundary.n_field_periods dtype: int64 - name: boundary.n_periodicity dtype: int64 - name: boundary.r_cos sequence: sequence: float64 - name: boundary.r_sin dtype: 'null' - name: boundary.z_cos dtype: 'null' - name: boundary.z_sin sequence: sequence: float64 - name: omnigenous_field_and_targets.id dtype: string - name: omnigenous_field_and_targets.json dtype: string - name: omnigenous_field_and_targets.aspect_ratio dtype: float64 - name: omnigenous_field_and_targets.major_radius dtype: float64 - name: omnigenous_field_and_targets.max_elongation dtype: float64 - name: omnigenous_field_and_targets.omnigenous_field.modB_spline_knot_coefficients sequence: sequence: float64 - name: omnigenous_field_and_targets.omnigenous_field.n_field_periods dtype: int64 - name: omnigenous_field_and_targets.omnigenous_field.poloidal_winding dtype: int64 - name: omnigenous_field_and_targets.omnigenous_field.torodial_winding dtype: int64 - name: omnigenous_field_and_targets.omnigenous_field.x_lmn sequence: sequence: sequence: float64 - name: omnigenous_field_and_targets.rotational_transform dtype: float64 - name: desc_omnigenous_field_optimization_settings.id dtype: string - name: desc_omnigenous_field_optimization_settings.json dtype: string - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.check_orientation dtype: bool - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.max_poloidal_mode dtype: int64 - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.max_toroidal_mode dtype: int64 - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.psi dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.aspect_ratio dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.elongation dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.is_iota_positive dtype: bool - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.is_stellarator_symmetric dtype: bool - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.major_radius dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.max_elongation dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.max_poloidal_mode dtype: int64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.max_toroidal_mode dtype: int64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.mirror_ratio dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.n_field_periods dtype: int64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.rotational_transform dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.torsion dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.aspect_ratio_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.aspect_ratio_settings.target_kind dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.aspect_ratio_settings.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.target_kind dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.eq_lcfs_grid_M_factor dtype: int64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.eq_lcfs_grid_N_factor dtype: int64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.eq_lcfs_grid_rho dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.eta_weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.rotational_transform_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.rotational_transform_settings.target_kind dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.rotational_transform_settings.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.optimizer_settings.maxiter dtype: int64 - name: desc_omnigenous_field_optimization_settings.optimizer_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.optimizer_settings.verbose dtype: int64 - name: vmec_omnigenous_field_optimization_settings.id dtype: string - name: vmec_omnigenous_field_optimization_settings.json dtype: string - name: vmec_omnigenous_field_optimization_settings.gradient_based_relative_objectives_tolerance dtype: float64 - name: vmec_omnigenous_field_optimization_settings.gradient_free_budget_per_design_variable dtype: int64 - name: vmec_omnigenous_field_optimization_settings.gradient_free_max_time dtype: int64 - name: vmec_omnigenous_field_optimization_settings.gradient_free_optimization_hypercube_bounds dtype: float64 - name: vmec_omnigenous_field_optimization_settings.infinity_norm_spectrum_scaling dtype: float64 - name: vmec_omnigenous_field_optimization_settings.max_poloidal_mode dtype: int64 - name: vmec_omnigenous_field_optimization_settings.max_toroidal_mode dtype: int64 - name: vmec_omnigenous_field_optimization_settings.n_inner_optimizations dtype: int64 - name: vmec_omnigenous_field_optimization_settings.use_continuation_method_in_fourier_space dtype: bool - name: vmec_omnigenous_field_optimization_settings.verbose dtype: bool - name: qp_init_omnigenous_field_optimization_settings.id dtype: string - name: qp_init_omnigenous_field_optimization_settings.json dtype: string - name: qp_init_omnigenous_field_optimization_settings.aspect_ratio dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.elongation dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.is_iota_positive dtype: bool - name: qp_init_omnigenous_field_optimization_settings.is_stellarator_symmetric dtype: bool - name: qp_init_omnigenous_field_optimization_settings.major_radius dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.mirror_ratio dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.n_field_periods dtype: int64 - name: qp_init_omnigenous_field_optimization_settings.torsion dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.id dtype: string - name: nae_init_omnigenous_field_optimization_settings.json dtype: string - name: nae_init_omnigenous_field_optimization_settings.aspect_ratio dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.max_elongation dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.max_poloidal_mode dtype: int64 - name: nae_init_omnigenous_field_optimization_settings.max_toroidal_mode dtype: int64 - name: nae_init_omnigenous_field_optimization_settings.mirror_ratio dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.n_field_periods dtype: int64 - name: nae_init_omnigenous_field_optimization_settings.rotational_transform dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.has_optimize_boundary_omnigenity_vmec_error dtype: bool - name: misc.has_optimize_boundary_omnigenity_desc_error dtype: bool - name: misc.has_generate_qp_initialization_from_targets_error dtype: bool - name: misc.has_generate_nae_initialization_from_targets_error dtype: bool - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 1240651097.3174775 num_examples: 182222 download_size: 610201645 dataset_size: 1240651097.3174775 - config_name: finite_beta_1pct features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.source_plasma_config_id dtype: string - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 76508664.04284965 num_examples: 112804 download_size: 52556502 dataset_size: 76508664.04284965 - config_name: finite_beta_2pct features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.source_plasma_config_id dtype: string - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 47402708.67692375 num_examples: 82722 download_size: 38593722 dataset_size: 47402708.67692375 - config_name: finite_beta_3pct features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.source_plasma_config_id dtype: string - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 25395079.54877086 num_examples: 55448 download_size: 25947395 dataset_size: 25395079.54877086 - config_name: finite_beta_4pct features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.source_plasma_config_id dtype: string - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 13509704.764567751 num_examples: 36444 download_size: 17086365 dataset_size: 13509704.764567751 - config_name: finite_beta_5pct features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: metrics.aspect_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: misc.vmecpp_wout_id dtype: string - name: misc.source_plasma_config_id dtype: string - name: misc.has_neurips_2025_forward_model_error dtype: bool - name: plasma_config_id dtype: string splits: - name: train num_bytes: 8792377.219300479 num_examples: 26729 download_size: 12538180 dataset_size: 8792377.219300479 - config_name: vmecpp_wout features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 - config_name: vmecpp_wout_finite_beta_1pct features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 - config_name: vmecpp_wout_finite_beta_2pct features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 - config_name: vmecpp_wout_finite_beta_3pct features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 - config_name: vmecpp_wout_finite_beta_4pct features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 - config_name: vmecpp_wout_finite_beta_5pct features: - name: plasma_config_id dtype: string - name: id dtype: string - name: json dtype: string splits: - name: train num_bytes: 1100757693175 num_examples: 148292 download_size: 956063943 dataset_size: 1100757693175 configs: - config_name: default data_files: - split: train path: data/train-* - config_name: finite_beta_1pct data_files: - split: train 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 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 ![Diagram of the computation of metrics of interest from a plasma boundary via the MHD equilibrium](assets/mhd_intro_v2.png) ### 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:
  • Plasma boundaries
  • Ideal MHD metrics in vacuum
  • Omnigenous field and targets, used as input for sampling of plasma boundaries
  • Sampling settings for various methods (DESC, VMEC, QP initialization, Near-axis expansion)
  • Miscellaneous information
    • the corresponding ideal MHD equilibrium ID in vmecpp_wout
    • errors that might have occurred during sampling or metrics computation.
 Contains:
  • For each plasma boundary in default, a JSON-string representation 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 corresponding plasma configuration ID in default
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:
  • Ideal MHD metrics with plasma
  • Miscellaneous information
    • the corresponding source plasma configuration ID in default
    • the corresponding ideal MHD equilibrium ID in vmecpp_wout_finite_beta_*pct
    • errors that might have occurred metrics computation.
 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`): ```python 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 ```python {'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](https://github.com/proximafusion/constellaration): `pip install constellaration` Load and instantiate plasma boundaries: ```python 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: ```python from constellaration.utils import visualization visualization.plot_surface(boundary).show() visualization.plot_boundary(boundary).get_figure().show() ``` Boundary | Cross-sections :-------------------------:|:-------------------------: ![Plot of plasma boundary](assets/boundary.png) | ![Plot of boundary cross-sections](assets/boundary_cross_sections.png) Stream and instantiate the VMEC ideal MHD equilibria: ```python 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: ```python from constellaration.utils import visualization visualization.plot_flux_surfaces(vmecpp_wout, boundary) ``` ![Plot of flux surfaces](assets/flux_surfaces.png) Save ideal MHD equilibrium to *VMEC2000 WOut* file: ```python 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: ```python 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](https://desc-docs.readthedocs.io/en/stable/) | Dynamical Equilibrium Solver for Confinement | | VMEC/[VMEC++](https://github.com/proximafusion/vmecpp) | 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 ## Dataset Card Contact alexbauer@proximafusion.com