Machine-learning models reproduced several important outputs from local, linear gyrokinetic simulations—computer calculations of how small plasma disturbances grow and oscillate—designed around a MAST-U-relevant pedestal parameter space, according to a version-1 preprint. On held-out simulations, the direct MH-MLP model predicted growth rate with an R-squared of 0.989 and a mean absolute error (MAE) of 0.649 in GENE-normalized units. MAE is a measure of the typical size of the model’s prediction error, so the result indicates close agreement for that target within the tested set.
The advantage was not the same for every target. A second model, called MH Class–Reg, first classified each case by its frequency and then sent it to a regressor for that class. It produced lower test-set MAE for real frequency and both diffusivity-ratio fingerprints—De/χe and χi/χe—than the direct MH-MLP: 1.33 versus 1.91 for frequency, 0.124 versus 0.161 for De/χe, and 0.117 versus 0.159 for χi/χe. The lower pointwise errors did not translate into a systematic improvement in R-squared.
How the simulation set was built
To create the cases, the researchers derived sampling bounds from Thomson-scattering measurements of MAST-U discharge 49108. They converted the sampled profiles into self-consistent equilibria with HELENA and post-processed them with CHEASE to generate the local gyrokinetic inputs used by GENE.
The workflow initialized 128 equilibria, of which 123 converged. After convergence and filtering, it left approximately 7,500 local simulations spanning six radial locations and 11 wavenumbers per equilibrium. These were generated simulation cases, rather than experimental observations.
Equilibrium-level splitting assigned 86 profiles to training, 12 to validation and 25 to testing. That corresponded to approximately 5,200, 800 and 1,600 simulations in the three groups, so the test measured performance on held-out equilibrium profiles rather than a random mix of points from every profile.
The models were asked to reproduce four kinds of output: growth rate, real frequency and the two diffusivity-ratio fingerprints, De/χe and χi/χe. The direct model predicted them together through separate output heads. The alternative first performed frequency classification, then used class-specific regressors; its training also combined classification and regression losses and used dropout regularization.
Where the models held up
The frequency classifier assigned the correct class to 92% of test samples. In an oracle test, where the true frequency class was supplied to the regressors, the MAE was 0.77 for frequency, 0.074 for De/χe and 0.069 for χi/χe. The corresponding R-squared values were 0.965, 0.923 and 0.908. The result identifies misclassification near regime boundaries as the main limitation of the full classification-regression pipeline.
On a scan of beta in an unseen equilibrium, both surrogates reproduced the broad trends of the underlying simulations. MH Class–Reg gave sharper regime transitions, while MH-MLP tended to overpredict growth at higher beta. The exact transition location in beta space was not reproduced.
On a denser, unseen radial-wavenumber grid, the models reproduced the overall instability structure and sharper regime transitions. Their transition locations, however, did not always coincide with the GENE results.
The model’s classification performance was also high under approximate KBM-like transport-fingerprint labels. MH Class–Reg reached overall accuracy of 0.98 and macro-F1 of 0.97, compared with 0.97 and 0.95 for MH-MLP. For the KBM-like class, recall improved from 0.86 to 0.91 and F1 from 0.91 to 0.95. Macro-F1 is a score that gives each class equal weight; because the labels were approximate and the class was imbalanced, these results do not amount to definitive mode identification.
A proof of principle, for now
Taken together, the authors present the approach as a proof of principle for reproducing several local, linear GENE outputs. They say broader sampling and further extensions are needed before wider application. The evidence therefore speaks to the modeled local simulations and their sampled parameter space, not to settings that were not tested.
The document is an arXiv version-1 preprint dated 26 August 2026. The work received EUROfusion and Euratom funding, partial support from the Research Council of Finland and computing resources from CSC.
Paper data and sources
Original title: Machine learning methods for modelling local, linear gyrokinetic simulations of MAST-U pedestal turbulence
Authors: Anna Niemelä, Daniel Jordan, Aaro Järvinen et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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