--- 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.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: 1235890475.515687 num_examples: 182222 download_size: 610097952 dataset_size: 1235890475.515687 - config_name: full_flat features: - name: metrics.id dtype: string - name: metrics.qi dtype: float64 - name: metrics.vacuum_well dtype: float64 - name: metrics.aspect_ratio dtype: float64 - name: metrics.max_elongation dtype: float64 - name: metrics.average_triangularity dtype: float64 - name: metrics.axis_magnetic_mirror_ratio dtype: float64 - name: metrics.edge_magnetic_mirror_ratio dtype: float64 - name: metrics.aspect_ratio_over_edge_rotational_transform dtype: float64 - name: metrics.flux_compression_in_regions_of_bad_curvature dtype: float64 - name: metrics.axis_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.edge_rotational_transform_over_n_field_periods dtype: float64 - name: metrics.minimum_normalized_magnetic_gradient_scale_length dtype: float64 - name: boundary.r_cos sequence: sequence: float64 - name: boundary.z_sin sequence: sequence: float64 - name: boundary.r_sin dtype: float64 - name: boundary.z_cos dtype: float64 - name: boundary.n_field_periods dtype: float64 - name: boundary.is_stellarator_symmetric dtype: bool - name: omnigenous_field_and_targets.id 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.rotational_transform dtype: float64 - name: omnigenous_field_and_targets.omnigenous_field.x_lmn sequence: sequence: sequence: float64 - name: omnigenous_field_and_targets.omnigenous_field.n_field_periods dtype: float64 - name: omnigenous_field_and_targets.omnigenous_field.poloidal_winding dtype: float64 - name: omnigenous_field_and_targets.omnigenous_field.torodial_winding dtype: float64 - name: omnigenous_field_and_targets.omnigenous_field.modB_spline_knot_coefficients sequence: sequence: float64 - name: desc_omnigenous_field_optimization_settings.id dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.elongation_settings.target_kind dtype: string - 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.omnigenity_settings.eta_weight dtype: float64 - 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.eq_lcfs_grid_M_factor dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.omnigenity_settings.eq_lcfs_grid_N_factor 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.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.aspect_ratio_settings.target_kind dtype: string - 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.weight dtype: float64 - name: desc_omnigenous_field_optimization_settings.objective_settings.rotational_transform_settings.target_kind dtype: string - name: desc_omnigenous_field_optimization_settings.optimizer_settings.name dtype: string - name: desc_omnigenous_field_optimization_settings.optimizer_settings.maxiter dtype: float64 - name: desc_omnigenous_field_optimization_settings.optimizer_settings.verbose dtype: float64 - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.psi dtype: float64 - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.check_orientation dtype: bool - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.max_poloidal_mode dtype: float64 - name: desc_omnigenous_field_optimization_settings.equilibrium_settings.max_toroidal_mode dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.torsion dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.elongation dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.aspect_ratio dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.major_radius dtype: float64 - 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: 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.max_elongation dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.max_poloidal_mode dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.max_toroidal_mode dtype: float64 - name: desc_omnigenous_field_optimization_settings.initial_guess_settings.rotational_transform dtype: float64 - name: vmec_omnigenous_field_optimization_settings.id dtype: string - name: vmec_omnigenous_field_optimization_settings.verbose dtype: bool - name: vmec_omnigenous_field_optimization_settings.max_poloidal_mode dtype: float64 - name: vmec_omnigenous_field_optimization_settings.max_toroidal_mode dtype: float64 - name: vmec_omnigenous_field_optimization_settings.n_inner_optimizations dtype: float64 - name: vmec_omnigenous_field_optimization_settings.gradient_free_max_time dtype: float64 - name: vmec_omnigenous_field_optimization_settings.infinity_norm_spectrum_scaling dtype: float64 - name: vmec_omnigenous_field_optimization_settings.gradient_free_budget_per_design_variable dtype: float64 - name: vmec_omnigenous_field_optimization_settings.use_continuation_method_in_fourier_space dtype: bool - name: vmec_omnigenous_field_optimization_settings.gradient_free_optimization_hypercube_bounds dtype: float64 - name: vmec_omnigenous_field_optimization_settings.gradient_based_relative_objectives_tolerance dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.id dtype: string - name: qp_init_omnigenous_field_optimization_settings.torsion dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.elongation dtype: float64 - name: qp_init_omnigenous_field_optimization_settings.aspect_ratio dtype: float64 - 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: 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: nae_init_omnigenous_field_optimization_settings.id dtype: string - name: nae_init_omnigenous_field_optimization_settings.aspect_ratio dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.mirror_ratio dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.max_elongation dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.n_field_periods dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.max_poloidal_mode dtype: float64 - name: nae_init_omnigenous_field_optimization_settings.max_toroidal_mode dtype: float64 - 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: 524176976 num_examples: 231021 download_size: 278511073 dataset_size: 524176976 - config_name: full_json features: - name: metrics.id dtype: string - name: metrics.json dtype: string - name: boundary.json dtype: string - name: omnigenous_field_and_targets.id dtype: string - name: omnigenous_field_and_targets.json dtype: string - name: desc_omnigenous_field_optimization_settings.id dtype: string - name: desc_omnigenous_field_optimization_settings.json dtype: string - name: vmec_omnigenous_field_optimization_settings.id dtype: string - name: vmec_omnigenous_field_optimization_settings.json dtype: string - name: qp_init_omnigenous_field_optimization_settings.id dtype: string - name: qp_init_omnigenous_field_optimization_settings.json dtype: string - name: nae_init_omnigenous_field_optimization_settings.id dtype: string - name: nae_init_omnigenous_field_optimization_settings.json dtype: string - 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: 906303072 num_examples: 231021 download_size: 453881947 dataset_size: 906303072 - config_name: vmecpp_ideal_mhd_equilibria features: - name: plasma_config_id dtype: string - name: vmecpp_wout_id dtype: string - name: vmecpp_wout_json dtype: string - name: __index_level_0__ dtype: int64 splits: - name: train num_bytes: 1373486837 num_examples: 324 download_size: 956063943 dataset_size: 1373486837 configs: - config_name: default data_files: - split: train path: data/train-* - config_name: full_flat data_files: - split: train path: full_flat/train-* - config_name: full_json data_files: - split: train path: full_json/train-* - config_name: vmecpp_ideal_mhd_equilibria data_files: - split: train path: vmecpp_ideal_mhd_equilibria/part-* license: mit language: - en tags: - physics - fusion - optimization - neurips pretty_name: ConStellaration size_categories: - 10K 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 ![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:** [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:
  • Plasma boundaries
  • Ideal MHD metrics
  • 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 about errors that might have occurred during sampling or metrics computation.
 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`): ```python 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 ```python {'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](https://github.com/proximafusion/constellaration): `pip install constellaration` Load and instantiate plasma boundaries: ```python 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: ```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 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: ```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")) ``` ## 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](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