Deep neural network Grad–Shafranov solver constrained with measured magnetic signals

Joung, Semin; Kim, Jaewook; Kwak, S.; Bak, J. G.; Lee, Sang-Gon; Han, Hyunsun; Lee, Geun-Ho; Kwon, Daeho; Ghim, Young-chul

doi:10.1088/1741-4326/ab555f

Cited by 44 publications

(31 citation statements)

References 65 publications

(93 reference statements)

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“…These combined benefits reduce the controller development cycle and accelerate the study of alternative plasma configurations. Indeed, artificial intelligence has recently been identified as a ‘Priority Research Opportunity’ for fusion control 14 , building on demonstrated successes in reconstructing plasma-shape parameters 15 , 16 , accelerating simulations using surrogate models 17 , 18 and detecting impending plasma disruptions 19 . RL has not, however, been used for magnetic controller design, which is challenging due to high-dimensional measurements and actuation, long time horizons, rapid instability growth rates and the need to infer the plasma shape through indirect measurements.…”

Section: Mainmentioning

confidence: 99%

Magnetic control of tokamak plasmas through deep reinforcement learning

Degrave

Felici

Buchli

et al. 2022

Nature

448

218

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Nuclear fusion using magnetic confinement, in particular in the tokamak configuration, is a promising path towards sustainable energy. A core challenge is to shape and maintain a high-temperature plasma within the tokamak vessel. This requires high-dimensional, high-frequency, closed-loop control using magnetic actuator coils, further complicated by the diverse requirements across a wide range of plasma configurations. In this work, we introduce a previously undescribed architecture for tokamak magnetic controller design that autonomously learns to command the full set of control coils. This architecture meets control objectives specified at a high level, at the same time satisfying physical and operational constraints. This approach has unprecedented flexibility and generality in problem specification and yields a notable reduction in design effort to produce new plasma configurations. We successfully produce and control a diverse set of plasma configurations on the Tokamak à Configuration Variable1,2, including elongated, conventional shapes, as well as advanced configurations, such as negative triangularity and ‘snowflake’ configurations. Our approach achieves accurate tracking of the location, current and shape for these configurations. We also demonstrate sustained ‘droplets’ on TCV, in which two separate plasmas are maintained simultaneously within the vessel. This represents a notable advance for tokamak feedback control, showing the potential of reinforcement learning to accelerate research in the fusion domain, and is one of the most challenging real-world systems to which reinforcement learning has been applied.

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Section: Mainmentioning

confidence: 99%

Magnetic control of tokamak plasmas through deep reinforcement learning

Degrave

Felici

Buchli

et al. 2022

Nature

448

218

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“…reinforcement learning (RL) based control). In fusion research, the use of NN models to compute the plasma topology [43][44][45] and to speed up slow workflows [46][47][48][49][50] is not a novel idea, nevertheless, to our knowledge this paper represents the first which effectively addresses the 3D MHD physics in W7-X scenarios.…”

Section: Applicationmentioning

confidence: 99%

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

et al. 2021

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In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations-usually done computationally-serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications (e.g. Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilibria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume-averaged normalized plasma pressure β (β = 2μ 0 p B 2 ) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional NNs are found to outperform feed-forward fully-connected NNs. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales.

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“…Similarly the reconstruction and reconstruction-control modes predict the same outputs, but use diagnostic information such as magnetic probes as inputs to the NN. Previous neural net equilibrium solvers [15][16][17][18][19][20][21][22] were developed in the spirit of reconstruction-control mode-mapping diagnostics to shaping parameters-with some exceptions such as [23] which reconstructs flux surfaces and [24] which is a fixedboundary solver. Similar to previous efforts on other machines, we obtain good predictions using the magnetic diagnostics.…”

Section: Introductionmentioning

confidence: 99%

Neural net modeling of equilibria in NSTX-U

Wai,

Boyer,

Kolemen

2022

Preprint

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Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade (NSTX-U) for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a freeboundary equilibrium solver trained on the EFIT01 reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The equilibrium neural network is trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, the NN can use magnetic diagnostics as inputs for equilibrium prediction thus acting as a reconstruction code, or can use profiles and external currents as inputs to act as a traditional free-boundary Grad-Shafranov solver. We report strong performance for both networks indicating that these models could reliably be used within closed-loop simulations. Some limitations regarding generalizability and noise are discussed.

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Deep neural network Grad–Shafranov solver constrained with measured magnetic signals

Cited by 44 publications

References 65 publications

Magnetic control of tokamak plasmas through deep reinforcement learning

Magnetic control of tokamak plasmas through deep reinforcement learning

Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

Neural net modeling of equilibria in NSTX-U

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