Daily Papers

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 offer a promising magnetic confinement approach for achieving controlled nuclear fusion. However, stellarator design remains challenging, as evaluating configuration performance requires computationally expensive, high-fidelity simulations. In particular, key performance metrics derived from guiding center simulations are costly to include directly in the design optimization loop, and are almost exclusively used as diagnostics. Machine learning has the potential to advance fusion research by enabling rapid generation and evaluation of new stellarator configurations. Effectively applying ML for fusion demands large-scale datasets that capture both design diversity and high-fidelity simulation outputs. In this work, we introduce the Benchmark of Stellarator Simulations (BoSS), a dataset of stellarator designs paired with guiding center simulation results and trajectories. The BoSS is the first large-scale dataset of guiding center simulations, containing simulation data for 180,000 distinct magnetohydrodynamic equilibria spanning a wide range of magnetic geometries and confinement properties. To exemplify the utility of ML to accelerate stellarator design, we formulate and address two sets of modeling tasks: generative modeling for designing stellarators with good particle confinement, and surrogate modeling for predicting stellarator heat deposition patterns and particle trajectories. The tasks reveal the potential impact ML can have in the stellarator field and important opportunities to improve the applicability of ML models in the sciences. Our baselines generate diverse, performant stellarators and provide useful surrogate predictions, and point to long-horizon trajectory forecasting and out-of-distribution generation as key directions for future work. The BoSS can be accessed through https://boss.flatironinstitute.org/.

Stellarators are fusion devices that use externally generated, three-dimensional magnetic fields to confine hot plasma and offer a promising route to commercial fusion. Their electromagnetic coils pose a challenging design problem: they must reproduce the target magnetic field while satisfying engineering constraints and remaining practical and cost-effective to manufacture. Finding suitable geometries is a highly nonlinear inverse problem that generally has neither a closed-form nor a unique solution. This problem lies at the heart of stellarator design. We introduce CoilStellaration, a dataset and benchmark for learning the mapping between coil geometries from target plasma magnetic fields and engineering requirements. The dataset contains 177,000 optimized filamentary coilsets targeting plasma equilibria from ConStellaration, with sampled engineering requirements and achieved geometric and magnetic-field metrics. It spans multiple coil counts and field-period numbers, supporting studies of both specialized and shared models across configurations. The benchmark asks models to predict coils conditioned on a target equilibrium and requirements on coil-coil and coil-plasma spacing, curvature, and magnetic-field error. We show that magnetic-field accuracy remains the main challenge, with learned models rarely satisfying all requirements simultaneously. However, using learned predictions to initialize conventional coil optimization can accelerate early progress. We release baseline models and evaluation code to support reproducible research on both direct coil generation and learned optimization initializations. By lowering the barrier for machine learning and optimization researchers to engage with stellarator coil design, we aim to accelerate progress toward practical, cost-effective stellarator power plants.

We present a fast, open-source calculation of the vacuum response matrix and surface inductance in non-axisymmetric geometries capable of running with up to 10^5 boundary points in tens of seconds on a laptop. Ideal magneto-hydrodynamic (MHD) stability modeling for free boundary modes requires the perturbed vacuum energy. We extend the VACUUM code to non-axisymmetric geometries in the new Julia implementation of the Generalized Perturbed Equilibrium Code, combining a collocation approach to the boundary integral equations with a high-order singularity correction scheme. The correction is recast into explicit quadrature weights acting on the collocation values, which allows the corrected operator to be assembled explicitly rather than applied to a given surface field, and the structure of that matrix under field-period and stellarator symmetry is then exploited to reduce storage and solve cost. We find that the vacuum response matrix converges at fourth order or greater in the grid spacing, reaching a given accuracy on a coarser grid than previous implementations without the high-order method. The non-axisymmetric calculation converges to the axisymmetric VACUUM result for a tokamak and the CAS3D result for a W7-X stellarator equilibrium. This work enables fast free boundary ideal MHD stability and perturbed equilibrium calculations in stellarators.

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.