Affiliation:
1. Numerical Methods in Plasma Physics Max Planck Institute for Plasma Physics Garching Germany
2. Department of Computer Science Technical University of Munich Garching Germany
3. Stellarator Dynamics and Transport Max Planck Institute for Plasma Physics Greifswald Germany
4. Institute of Theoretical and Computational Physics Graz University of Technology Graz Austria
Abstract
AbstractIn 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.
Cited by
2 articles.
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1. Magnetohydrodynamic Equilibrium Reconstruction with Consistent Uncertainties;The 42nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering;2023-11-27
2. Special issue: Machine learning methods in plasma physics;Contributions to Plasma Physics;2023-06