ConStellaration: A dataset of QI-like stellarator plasma boundaries and optimization benchmarks

Abstract

Stellarators are magnetic confinement devices under active development 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. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader 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, considered as a promising path to commercial fusion due to their inherent resilience to current driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset along with benchmark problems and baselines, we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.

Figures (13)

• Figure 1: Examples of diverse stellarator plasma boundaries.
• Figure 2: A plasma boundary is defined by the coefficients $R_{mn}$ and $Z_{mn}$ of a truncated Fourier series in cylindrical coordinates, parametrized by the lab-frame poloidal angle $\theta$ and toroidal angle $\phi$. This boundary is passed to the VMEC++ code hirshman1983steepestschilling2025numerics to compute an ideal- equilibrium. In this example, the configuration is stellarator symmetric, meaning that $R(\theta,\phi) = R(-\theta,-\phi)$ and $Z(\theta,\phi) = -\,Z(-\theta,-\phi)$, and the number of repeated field periods ($N_{\mathrm{fp}}$) is four. The ideal- equilibrium defines the magnetic field throughout the plasma volume, comprising nested magnetic flux surfaces on which magnetic field lines (depicted in white) lie. We can then compute various metrics of interest from the equilibrium field.
• Figure 3: Visualization of the iso-contours of the magnetic field strength $B$ and a few magnetic field lines (black). In the Boozer coordinate system boozer1981plasma, the original poloidal and toroidal angles are transformed into Boozer angles $\theta_{B}$ and $\phi_{B}$, respectively, to straighten the magnetic field lines (black).
• Figure 4: Four optimized samples from our dataset with 1, 2, 4, and 5 field periods. A finite computational budget for each sample generation leads to an approximate field at the plasma boundary. All field plots share the same color bar and the boundary cross-section labels correspond to those in Figure \ref{['fig:intro_mhd']}.
• Figure 5: Diverse plasma configurations obtained for the same targets. Optimization methods vary in initialization strategy, framework, and settings. While some runs favor matching the target field and mirror ratio, other runs better match the remaining target properties.