Bayesian uncertainty calculation in neural network inference of ion and electron temperature profiles at W7X
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 Xray imaging diagnostic at W7X. 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:

 MaxPlanckInst. for Plasma Physics, Greifswald (Germany)
 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 7X 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 00346748
 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 W7X. 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 W7X. 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 W7X". 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 W7X},
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 Xray imaging diagnostic at W7X. 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}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Argon impurity transport studies at Wendelstein 7X using xray imaging spectrometer measurements
journal, June 2017
 Langenberg, A.; Pablant, N. A.; Marchuk, O.
 Nuclear Fusion, Vol. 57, Issue 8
Overview of diagnostic performance and results for the first operation phase in Wendelstein 7X (invited)
journal, October 2016
 Krychowiak, M.; Adnan, A.; Alonso, A.
 Review of Scientific Instruments, Vol. 87, Issue 11
Forward Modeling of XRay Imaging Crystal Spectrometers Within the Minerva Bayesian Analysis Framework
journal, April 2016
 Langenberg, A.; Svensson, J.; Thomsen, H.
 Fusion Science and Technology, Vol. 69, Issue 2
Analysis of JET charge exchange spectra using neural networks
journal, January 1999
 Svensson, J.; Hellermann, M. von; König, R. W. T.
 Plasma Physics and Controlled Fusion, Vol. 41, Issue 2
Bayesian approach to neuralnetwork modeling with input uncertainty
journal, January 1999
 Wright, W. A.
 IEEE Transactions on Neural Networks, Vol. 10, Issue 6
The Set of Diagnostics for the First Operation Campaign of the Wendelstein 7X Stellarator
journal, October 2015
 König, Ralf; Baldzuhn, J.; Biel, W.
 Journal of Instrumentation, Vol. 10, Issue 10
Gradientbased learning applied to document recognition
journal, January 1998
 Lecun, Y.; Bottou, L.; Bengio, Y.
 Proceedings of the IEEE, Vol. 86, Issue 11
A prediction tool for realtime application in the disruption protection system at JET
journal, October 2007
 Cannas, B.; Fanni, A.; Sonato, P.
 Nuclear Fusion, Vol. 47, Issue 11
Works referencing / citing this record:
Bayesian modeling of microwave radiometer calibration on the example of the Wendelstein 7X electron cyclotron emission diagnostic
journal, April 2019
 Hoefel, Udo; Hirsch, Matthias; Kwak, Sehyun
 Review of Scientific Instruments, Vol. 90, Issue 4
Neural network approximation of Bayesian models for the inference of ion and electron temperature profiles at W7X
journal, May 2019
 Pavone, A.; Svensson, J.; Langenberg, A.
 Plasma Physics and Controlled Fusion, Vol. 61, Issue 7
Figures / Tables found in this record: