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Title: Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X

Abstract

We make use of a Bayesian description of the neural network (NN) training for the calculation of the uncertainties in the NN prediction. Having uncertainties on the NN prediction allows having a quantitative measure for trusting the NN outcome and comparing it with other methods. Within the Bayesian framework, the uncertainties can be calculated under different approximations. The NN has been trained with the purpose of inferring ion and electron temperature profile from measurements of a X-ray imaging diagnostic at W7-X. The NN has been trained in such a way that it constitutes an approximation of a full Bayesian model of the diagnostic, implemented within the Minerva framework. Finally, the network has been evaluated using measured data and the uncertainties calculated under different approximations have been compared with each other, finding that neglecting the noise on the NN input can lead to an underestimation of the error bar magnitude in the range of 10%–30%.

Authors:
 [1];  [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Max-Planck-Inst. for Plasma Physics, Greifswald (Germany)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
Contributing Org.:
Wendelstein 7-X Team
OSTI Identifier:
1473874
Grant/Contract Number:  
633053
Resource Type:
Accepted Manuscript
Journal Name:
Review of Scientific Instruments
Additional Journal Information:
Journal Volume: 89; Journal Issue: 10; Journal ID: ISSN 0034-6748
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Pavone, A., Svensson, J., Langenberg, A., Pablant, N., Hoefel, U., Kwak, S., and Wolf, R. C. Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X. United States: N. p., 2018. Web. doi:10.1063/1.5039286.
Pavone, A., Svensson, J., Langenberg, A., Pablant, N., Hoefel, U., Kwak, S., & Wolf, R. C. Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X. United States. doi:10.1063/1.5039286.
Pavone, A., Svensson, J., Langenberg, A., Pablant, N., Hoefel, U., Kwak, S., and Wolf, R. C. Fri . "Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X". United States. doi:10.1063/1.5039286. https://www.osti.gov/servlets/purl/1473874.
@article{osti_1473874,
title = {Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7-X},
author = {Pavone, A. and Svensson, J. and Langenberg, A. and Pablant, N. and Hoefel, U. and Kwak, S. and Wolf, R. C.},
abstractNote = {We make use of a Bayesian description of the neural network (NN) training for the calculation of the uncertainties in the NN prediction. Having uncertainties on the NN prediction allows having a quantitative measure for trusting the NN outcome and comparing it with other methods. Within the Bayesian framework, the uncertainties can be calculated under different approximations. The NN has been trained with the purpose of inferring ion and electron temperature profile from measurements of a X-ray imaging diagnostic at W7-X. The NN has been trained in such a way that it constitutes an approximation of a full Bayesian model of the diagnostic, implemented within the Minerva framework. Finally, the network has been evaluated using measured data and the uncertainties calculated under different approximations have been compared with each other, finding that neglecting the noise on the NN input can lead to an underestimation of the error bar magnitude in the range of 10%–30%.},
doi = {10.1063/1.5039286},
journal = {Review of Scientific Instruments},
number = 10,
volume = 89,
place = {United States},
year = {2018},
month = {7}
}

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Figures / Tables:

Figure 1 Figure 1: The average value of the relative uncertainty calculated with (orange bars) and without (green bars) input noise contribution for both Te (left) and Ti (right) profiles, as found from data collected across different experiments.

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Works referenced in this record:

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