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Machine learning methods for modelling local, linear gyrokinetic simulations of MAST-U pedestal turbulence

This paper develops and evaluates machine learning surrogate models trained on local linear GENE simulations to rapidly predict gyrokinetic stability metrics for MAST-U pedestal turbulence, demonstrating that a multi-head classification-regression approach effectively captures regime-dependent transport behaviors to accelerate integrated pedestal modeling.

Original authors: Anna Niemelä, Daniel Jordan, Aaro Järvinen, Amanda Bruncrona, Adam Kit, Lorenzo Frassinetti, David Hatch, Leonhard Leppin, Samuli Saarelma, the MAST Upgrade team, EUROfusion Tokamak Exploitation team

Published 2026-08-27

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CC BY 4.0

Original authors: Anna Niemelä, Daniel Jordan, Aaro Järvinen, Amanda Bruncrona, Adam Kit, Lorenzo Frassinetti, David Hatch, Leonhard Leppin, Samuli Saarelma, the MAST Upgrade team, EUROfusion Tokamak Exploitation team

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quest to build a power plant that runs on the same fuel as the stars, scientists are trying to contain superheated gas, known as plasma, inside a magnetic bottle. To get enough energy out of this fusion reaction, the plasma must be kept under immense pressure. In the most successful operating mode, a thick, high-pressure wall of gas forms at the very edge of the plasma, acting like a protective barrier that keeps the core hot and dense. This wall is called the pedestal. If the pedestal is too weak, the heat escapes too quickly; if it is too strong, it can become unstable and crash, dumping energy onto the reactor walls. Predicting exactly how high and wide this pedestal can grow is one of the most difficult challenges in fusion science, because it depends on a chaotic mix of tiny, swirling currents within the gas that are incredibly hard to calculate.

For decades, researchers have relied on simplified rules of thumb to guess how this edge barrier will behave, but these shortcuts often miss the complex physics happening at the microscopic level. To get a true picture, scientists use powerful computer codes that simulate the motion of individual particles as they spiral along magnetic field lines. These simulations are so detailed and computationally expensive that running them for every possible scenario would take years, making them impractical for designing future reactors. A team of researchers, led by Anna Niemelä at VTT Technical Research Centre of Finland, has now developed a new way to speed up this process. They trained artificial intelligence models to act as fast, accurate stand-ins for these heavy-duty simulations, specifically for the turbulent conditions found in the edge of the MAST-U spherical tokamak, a unique fusion device in the United Kingdom.

The researchers started by creating a massive library of data. They took real measurements from a specific experiment on the MAST-U machine and used them to define the boundaries of what a realistic plasma edge looks like. Instead of just copying the exact data, they generated thousands of slightly different, physically consistent plasma profiles by varying the temperature and density at the edge. For each of these profiles, they ran a sophisticated simulation code called GENE to calculate how the plasma would react to small disturbances. These calculations produced a set of outcomes: how fast instabilities would grow, how fast the waves would move, and how efficiently heat and particles would leak out. This process resulted in a dataset of roughly 7,500 individual simulation points, covering a wide range of conditions that might occur in the real machine.

With this library in hand, the team trained two different types of machine learning models to learn the relationship between the input conditions and the simulation results. The first model was a standard neural network designed to predict all the outcomes at once. It worked very well at predicting how fast the instabilities would grow, but it struggled with the more complex patterns of heat and particle leakage. These leakage patterns tend to cluster into distinct groups depending on the type of turbulence, and the standard model tended to blur the lines between them, producing vague averages instead of sharp, clear distinctions.

To solve this, the team built a second, more specialized model that first sorts the plasma conditions into different categories based on how the waves move, and then uses a separate calculator for each category. This approach allowed the model to recognize that different types of turbulence behave in fundamentally different ways. When tested, this new method was much better at capturing the sharp transitions between these different regimes. It could predict the specific ratios of heat and particle loss with much greater accuracy, correctly identifying when the plasma was behaving like a specific type of unstable mode known as a kinetic ballooning mode. This mode is particularly important because it is often the limit that determines how high the pressure pedestal can climb before it collapses.

The study shows that these artificial intelligence models can reproduce the results of the heavy-duty physics simulations with remarkable speed and accuracy, provided they are given enough data to learn the distinct behaviors of different turbulence types. While the models are not perfect and still face challenges when the plasma conditions are right on the edge of changing from one type of behavior to another, they represent a significant step forward. By replacing the slow, expensive calculations with these fast surrogates, scientists can now run the complex physics needed for reactor design in a fraction of the time. This opens the door to more detailed and reliable predictions of how the edge of a fusion plasma will behave, bringing the goal of a stable, high-performance fusion reactor one step closer to reality.

Technical Summary: Machine Learning Methods for Modelling Local, Linear Gyrokinetic Simulations of MAST-U Pedestal Turbulence

Problem Statement
In high-confinement (H-mode) tokamak plasmas, the edge transport barrier (pedestal) significantly influences core pressure and fusion performance. Predicting pedestal height and width typically relies on reduced models, such as EPED, which assume the pedestal is limited by kinetic ballooning modes (KBMs) or ideal-MHD peeling instabilities. However, these models often employ simplified transport assumptions that may not fully capture the complexity of microturbulence-driven transport.

High-fidelity gyrokinetic (GK) codes like GENE can model microinstabilities (e.g., ITG, TEM, KBM) and turbulent transport with greater physical fidelity. Nevertheless, the computational cost of GK simulations—particularly nonlinear ones, but also the extensive linear scans required for quasilinear transport models—prohibits their routine use in integrated modeling, scenario optimization, or real-time analysis. There is a need for surrogate models that can provide gyrokinetic-based inputs to reduced transport models at speeds comparable to current reduced models while retaining a closer connection to kinetic physics.

Methodology
The authors developed a machine learning (ML) framework to create surrogate models for local, linear gyrokinetic simulations within a parameter space relevant to the MAST Upgrade (MAST-U) spherical tokamak.

Dataset Generation:
- Sampling Strategy: Instead of sampling local gyrokinetic inputs directly, the authors varied global pedestal profile parameters (pedestal top temperature and density, separatrix density, and profile widths) within bounds derived from Thomson scattering measurements of MAST-U discharge 49108.
- Equilibrium Construction: These sampled profiles were used to construct smooth temperature and density profiles via an m-tanh parameterization. These were input into the HELENA equilibrium solver to generate self-consistent Grad–Shafranov equilibria, including bootstrap current effects. This approach ensures physically plausible combinations of plasma profiles, geometry, and stability parameters while reducing the dimensionality of the data-generation problem.
- Gyrokinetic Simulations: For 123 converged equilibria, local linear GENE simulations were performed at six radial locations across the pedestal and eleven ion-scale binormal wavenumbers ( $k_y\rho_s$ ). This yielded a dataset of approximately 7,500 simulations.
- Targets: The models were trained to predict linear growth rates ( $\gamma$ ), real frequencies ( $\omega$ ), and diffusivity ratios ( $D_e/\chi_e$ and $\chi_i/\chi_e$ ), which serve as transport fingerprints for different instability regimes.
Model Architectures:
- Multi-Head Multilayer Perceptron (MH-MLP): A standard deep learning approach using shared hidden layers followed by separate output heads for each target quantity. This architecture assumes a smooth mapping between inputs and outputs.
- Multi-Head Classification–Regression (MH Class–Reg): Recognizing that diffusivity ratios and frequencies exhibit clustered, regime-dependent behavior with sharp transitions, a hybrid model was developed. This model first classifies samples into three frequency-based regimes ( $\omega < -1$ , $-1 \le \omega \le 1$ , $\omega > 1$ ) and then applies class-specific multi-head regressors to predict the targets. This aims to capture sharp transitions associated with changes in the dominant instability mode.

Key Results

MH-MLP Performance: The direct MH-MLP accurately reproduced the linear growth rate ( $R^2 \approx 0.99$ ) and provided reasonable predictions for real frequency. However, it struggled with the diffusivity ratios, producing diffuse predictions that failed to preserve the clustered structure of the GENE data. The model tended to smooth over sharp transitions between instability regimes.
MH Class–Reg Performance: The classification–regression approach significantly reduced the mean absolute error (MAE) for the clustered targets ( $\omega$ $ω$ , $D_e/\chi_e$ $D_{e} / χ_{e}$ , $\chi_i/\chi_e$ $χ_{i} / χ_{e}$ ). It successfully reproduced sharper transitions in structured scans (e.g., beta scans and dense radial/wavenumber grids).
- The frequency-based classifier achieved 92% accuracy on the test set.
- "Oracle" tests (where the true regime class was provided to the regressor) showed substantially lower MAE and higher $R^2$ , indicating that the class-specific regressors are capable of accurate modeling within regimes, but the full pipeline's performance is limited by the robustness of the classification step near regime boundaries.
KBM Identification: Using transport-fingerprint criteria ( $D_e/\chi_e \approx 2/3$ , $\chi_i/\chi_e \approx 1$ , and ion diamagnetic frequency), the MH Class–Reg model achieved a macro-F1 score of 0.97 for identifying KBM-like modes, outperforming the MH-MLP (0.95). It improved the recall for KBM-like points from 0.86 to 0.91.

Significance and Limitations
The paper demonstrates that machine learning surrogates can effectively reproduce key outputs of local linear gyrokinetic simulations, offering a pathway to integrate kinetic stability information into reduced pedestal models with reduced computational cost. The study highlights that while growth rates can be modeled smoothly, transport fingerprints exhibit regime-dependent clustering that benefits from classification-based architectures.

The authors maintain a modest scope, noting several limitations:

Scope of Physics: The dataset is restricted to ion-scale wavenumbers and local linear simulations; it does not include electron-scale turbulence, multi-scale effects, or nonlinear saturation.
Parameter Space: The model is trained on a single MAST-U discharge with fixed equilibrium shape, magnetic field, and current. While this serves as a proof-of-principle, generalization to broader operational regimes requires future expansion of the training data.
Local Approximation: The use of the local flux-tube approximation in the steep-gradient pedestal region is acknowledged as a simplification that may not be fully justified, though it is considered acceptable for this initial study.
Classification Limitations: The frequency-based classification is a simplified proxy for mode identification. The authors suggest that future work could explore more detailed mode classifications and probabilistic treatments of the classification step to better handle transition regions.

The work concludes that while the surrogate models successfully capture the dominant physics and instability fingerprints, further development is required to expand the operational space and refine the handling of regime transitions before broad application in integrated modeling workflows.

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