Research article

Comparing theory based and higher-order reduced models for fusion simulation data

  • Received: 09 November 2018 Accepted: 23 November 2018 Published: 06 December 2018
  • We consider using regression to fit a theory-based log-linear ansatz, as well as higher order approximations, for the thermal energy confinement of a Tokamak as a function of device features. We use general linear models based on total order polynomials, as well as deep neural networks. The results indicate that the theory-based model fits the data almost as well as the more sophisticated machines, within the support of the data set. The conclusion we arrive at is that only negligible improvements can be made to the theoretical model, for input data of this type.

    Citation: David E. Bernholdt, Mark R. Cianciosa, David L. Green, Kody J.H. Law, Alexander Litvinenko, Jin M. Park. Comparing theory based and higher-order reduced models for fusion simulation data[J]. Big Data and Information Analytics, 2018, 3(2): 41-53. doi: 10.3934/bdia.2018006

    Related Papers:

  • We consider using regression to fit a theory-based log-linear ansatz, as well as higher order approximations, for the thermal energy confinement of a Tokamak as a function of device features. We use general linear models based on total order polynomials, as well as deep neural networks. The results indicate that the theory-based model fits the data almost as well as the more sophisticated machines, within the support of the data set. The conclusion we arrive at is that only negligible improvements can be made to the theoretical model, for input data of this type.


    加载中
    [1] Christopher MB (2006) Pattern recognition and machine learning. J Electron Imaging 16: 140–155.
    [2] Boyd S, Vandenberghe V (2004) Convex optimization, Cambridge university press.
    [3] Goodfellow I, Bengio Y, Courville A (2016) Deep Learning, MIT Press.
    [4] Kushner H, Yin GG (2003) Stochastic approximation and recursive algorithms and applications, Springer Science & Business Media, 35.
    [5] Mallat S (2016) Understanding deep convolutional networks. Phil Trans R Soc A 374: 20150203. doi: 10.1098/rsta.2015.0203
    [6] Moosavi-Dezfooli SM, Fawzi A, Frossard P (2016) Deepfool: A simple and accurate method to fool deep neural networks, In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2574–2582.
    [7] Murphy KP (2014) Machine learning: A probabilistic perspective. CHANCE 27: 62–63.
    [8] Park JM, Ferron JR , Holcomb CT, et al. (2018) Integrated modeling of high βn steady state scenario on diii-d. Phys Plasmas 25: 012506. doi: 10.1063/1.5013021
    [9] Park JM, Staebler G, Snyder PB, et al. (2018) Theory-based scaling of energy confinement time for future reactor design. Available from: http://ocs.ciemat.es/EPS2018ABS/pdf/P5.1096.pdf.
    [10] Rasmussen CE (2003) Gaussian processes in machine learning, MIT Press.
    [11] Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat: 400–407.
    [12] Snyder PB, Burrell KH,Wilson HR, et al. (2007) Stability and dynamics of the edge pedestal in the low collisionality regime: Physics mechanisms for steady-state elm-free operation. Nucl Fusion 47: 961. doi: 10.1088/0029-5515/47/8/030
    [13] Staebler GM, Kinsey JE, Waltz RE (2007) A theory-based transport model with comprehensive physics. Phys Plasmas 14: 055909. doi: 10.1063/1.2436852
  • Reader Comments
  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2012) PDF downloads(1664) Cited by(0)

Article outline

Figures and Tables

Figures(5)  /  Tables(2)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog