Development of a non-parametric Gaussian process model in the three-dimensional equilibrium reconstruction code V3FIT

Howell, Eric; Hanson, J.D.

doi:10.1017/s0022377819000813

Cited by 12 publications

(11 citation statements)

References 17 publications

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“…Finally, the use of MHD fast surrogate models can impact multiple applications: fast Bayesian inference of plasma parameters and equilibrium reconstruction workflows for intra-shot analysis 6 , access to large and rich optimization spaces for present and future magnetic confinement devices, milliseconds-range MHD equilibrium computations for realtime plasma control, and the generation of very large data sets of equilibrium computations necessary to investigate machine learning control strategies (e.g. RL) 7 .…”

Section: Discussionmentioning

confidence: 99%

“…If target physics quantities are not adequately reproduced by the surrogate model, a two-stage approach should be pursued: employ the model predictions to extensively explore the target input space, then, switch to a high-fidelity equilibrium computation to refine the solution. This may be applied to provide fast transformations for diagnostics, a broad exploration of the posterior probability distribution in a Bayesian framework, or good initial configurations for a more rapid convergence of equilibrium codes 7. It is important to note that when a sufficiently large data set is accessible, given the relative low training time, the proposed NN models could be trained to target specific data distributions expected for a use case application, thus reducing the covariate shift between the training and test set.…”

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confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

mentioning

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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“…The resulting reconstructed equilibria may give insight into unmeasurable or hard-to-measure quantities [7] and often form the basis for subsequent analyses. [8,9] Hence, suitable error estimates for the reconstructed parameters are of interest. Two core elements of the forward model for the reconstruction process are the actual equilibrium solver and the mapping of an equilibrium solution to corresponding experimental diagnostics.…”

Section: Equilibrium Reconstructionmentioning

confidence: 99%

Uncertainty quantification in three‐dimensional magnetohydrodynamic equilibrium reconstruction via surrogate‐assisted Bayesian inference

Köberl,

von Toussaint,

Bungartz

et al. 2023

Contributions to Plasma Physics

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In three‐dimensional (3D) equilibrium, reconstruction defining parameters of an ideal magneto‐hydrodynamic equilibrium are inferred from a set of plasma diagnostic measurements. For the reconstructed parameters, various forms of uncertainty estimates exist within common 3D reconstruction frameworks. These estimates often assume a Gaussian posterior distribution. The validity of this assumption is not obvious in such highly nonlinear inverse problems, and therefore the accuracy of the estimates cannot be guaranteed. In this work, we formulate the problem of 3D equilibrium reconstruction in a Bayesian sense and explore the posterior distribution of reconstruction parameters via Markov chain Monte Carlo (MCMC) sampling. The target reconstruction parameters, that is, shape and scaling factors of the pressure and toroidal current‐density profiles as well as the total toroidal flux, are taken from a reduced subspace of Wendelstein 7‐X equilibrium configurations. Since the corresponding forward model evaluations are computationally demanding, we replace the forward model via a polynomial chaos expansion surrogate. We compare the posterior distribution obtained via MCMC sampling to Laplace's approximation, which assumes a Gaussian posterior. We find that the two approaches provide similar results in regimes where the uncertainty on the plasma diagnostic signals is low. However, discrepancies between the posteriors are observed in cases of higher diagnostic signal uncertainty. Therefore, we provide further validation of the commonly used Laplace's approximation as a method of uncertainty quantification in 3D equilibrium reconstruction and showcase some of its limitations.

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“…While data-driven methods have been utilized in many contexts and for many purposes-such as for identifying error estimates in sophisticated validation studies using traditional physics simulations models [379,380], as well as being used in semi-empirical methods [381], stabilization analysis [382], the development of plasma stability control techniques [383], discharge control systems [384], deep statistical inference models on experimental data [385][386][387], as well as feedback control schemes [388]many of these techniques are frequently considered more empirical than physics-based.…”

Section: B Data-driven Physics Modelsmentioning

confidence: 99%

2022 Review of Data-Driven Plasma Science

Archibald¹,

Asif²,

Becker³

et al. 2022

Preprint

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Data science and technology offer transformative tools and methods to science. This review article highlights latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS). A large amount of data and machine learning algorithms go hand in hand. Most plasma data, whether experimental, observational or computational, are generated or collected by machines today. It is now becoming impractical for humans to analyze all the data manually. Therefore, it is imperative to train machines to analyze and interpret (eventually) such data as intelligently as humans but far more efficiently in quantity. Despite the recent impressive progress in applications of data science to plasma science and technology, the emerging field of DDPS is still in its infancy. Fueled by some of the most challenging problems such as fusion energy, plasmaprocessing of materials, and fundamental understanding of the universe through observable plasma phenomena, it is expected that DDPS continues to benefit significantly from the interdisciplinary marriage between plasma science and data science into the foreseeable future. CONTENTSI. Introduction 6 II. Fundamental Data Science 6 A. Introduction 6 B. Data Reduction/Compression 7 C. Dimensional reduction and sparse modeling 8 D. ML-enhanced modeling and simulation 9 E. ML Hardware and integration with models 10 F. Workflow Automation 11 G. Uncertainty Quantification 12 H. Visualization and Data Understanding 13 I. ML Control Theory 15 III. Basic Plasma Physics and Laboratory Experiments A. Introduction B. Spectroscopy, imaging and tomography C. Sparse measurement and noise D. Synthetic instruments and data E. Experimental data visualization F. High-rep rate laser experiments G. Charged particle beams H. Control and Optimisation of Plasma Accelerator Experiments I. Dusty and complex plasmas J. Physics and machine learning K. Challenges and outlook 5 IV. Magnetic Confinement Fusion 36 A. Introduction 36 B. Data-Driven Physics Models 36 C. Optimizing experimental workflows with data-driven methods 37 D. Diagnostics and Fusion Data Streams 38 E. Prediction of Tokamak Disruption 39 F. Surrogate models of fusion plasma 40 G. Magnetic Fusion Energy Data Challenges and Solutions 41 H. Data Science for extreme scale simulation 43 I. Challenges and outlook 44 V. Inertial confinement fusion and high-energy-density physics 45 A. Introduction 45 B. Representation learning for multimodal data 45 C. Transfer learning for simulation and experimen 47 D. Uncertainty quantification and Bayesian inference 47 E. High-performance computing and simulation acceleration 49 F. Design exploration and optimization 49 G. Self-driving experimental facilities 51 H. Challenges and outlook 52 VI. Space and astronomical plasmas 52 A. Introduction 52 B. Space and ground instruments 53 C. Space weather prediction 55 D. Transfer learning to improve historic data 56 E. Surrogate models of fluid closures using machine learning 56 F. Magnetic reconnection 58 G. Challenges and outlook 60 VII. Plasma tec...

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Development of a non-parametric Gaussian process model in the three-dimensional equilibrium reconstruction code V3FIT

Cited by 12 publications

References 17 publications

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

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

Uncertainty quantification in three‐dimensional magnetohydrodynamic equilibrium reconstruction via surrogate‐assisted Bayesian inference

2022 Review of Data-Driven Plasma Science

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