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 currentdriven 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 singleobjective 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.

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.

Stellarators are inherently steady-state plasma confinement devices, which is among the key reasons behind their renaissance as promising candidates for fusion power plants. Ideal MHD equilibria are a central part in optimising the complex, three-dimensional plasma shapes which are a necessary condition for steady-state operation of such devices. The equilibrium magnetic field is required not only in optimisation but also plays a role in future real-time control algorithms and simulation frameworks (Schissel et al. 2025). Solving the three-dimensional MHD equations requires numerical approaches, because no analytical solutions throughout the full volume of ideal MHD equilibria with nested magnetic topology exists yet (Bruno & Laurence 1996). Recent work advanced analytical models for Fourier components of the equilibrium magnetic field in a subset of reactor-relevant magnetic fields and analytical expansions close to the magnetic axis are used extensively in research (Nikulsin et al. 2024; Sengupta et al. 2024). These analytical solutions and the following numerical solvers assume nested magnetic topology, or inte-grability throughout the volume, and computation of chaotic regions or magnetic islands takes considerably more effort (Hudson et al. 2012). Accuracy of numerical PDE solutions is inherently connected to the representation which defines gradients, and commonly used ideal MHD equilibrium solvers with nested magnetic field topology can be differentiated accordingly: A widely used finite-difference solver employed in the design of currently operating stellarator devices is VMEC (Hirshman & Whitson 1983), another pseudo spectral solver is DESC (Dudt & Kolemen 2020) and a third example is GVEC (Hindenlang et al. 2025), that abstracts the notion of basis functions, which enabled computation of plasmas with figure-8 shape (Plunk et al. 2025). Email address for correspondence: timo.thun@ipp.mpg.de

The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite plasma beta, and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favorable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.