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

NeurIPS 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Machine learning for physical simulation · 1 citations (OpenAlex)

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Releases ConStellaration, a ~158k-sample dataset of QI-like stellarator plasma boundaries with VMEC++ ideal-MHD equilibria, three optimization benchmarks with classical baselines, and an MCMC-based generative sampler of feasible configurations.

Problem

Stellarator stage-one design is a high-dimensional constrained optimization problem with expensive physics simulations, and lacks standardized benchmarks and datasets for data-driven methods, especially for quasi-isodynamic (QI) configurations.

Approach

Generate a large dataset of diverse QI-like plasma boundaries by sampling omnigenous target fields and optimizing boundaries with DESC and VMEC++, then define three constrained benchmarks (geometric, simple-to-build QI, MHD-stable QI) with classical baselines and a PCA+random-forest+GMM+MCMC generator that samples feasible shapes without the physics oracle.

Key results

• ALM-NGOpt was the only baseline to find feasible solutions; geometric problem score 0.969 and simple-to-build score 0.431, MHD-stable score 130.0.
• MLP ensemble predicts target metrics from boundary coefficients with R^2 > 0.97 and RMSE < 0.1 for all metrics on the held-out set.
• The dataset contains about 158k evaluated configurations, with 1 to 5 field periods (15k, 20k, 68k, 27k, 28k respectively).

Measured effects reported in the paper

Surprising findings

• Both SciPy-based optimizers (trust-constr and COBYQA) failed to produce feasible solutions on the benchmarks, with only the ALM-NGOpt gradient-free method succeeding.
• Only 41 and 52 feasible points existed in the dataset for the relaxed geometric and simple-to-build problems (out of ~160k), motivating the generative sampler.

Limitations

• The degree of QI in the dataset is limited by the finite-budget optimization-based sampling process.
• The dataset covers only plasma boundaries and not electromagnetic coils or other reactor systems.
• Surrogate models are prone to extrapolation errors far from the training distribution.

Experimental setup

Datasets: ConStellaration dataset (~158k QI-like boundaries)

Benchmarks: ConStellaration optimization benchmarks (geometric, simple-to-build QI, MHD-stable QI)

Metrics: max elongation minimum normalized magnetic gradient scale length hypervolume normalized constraint violation RMSE R^2 NRMSE SNR

Baselines: scipy-trust-constr scipy-COBYQA ALM-NGOpt

Builds on: VMEC VMEC++ DESC SIMSOPT pyQSC

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