Big Data and Information Analytics, 2018, 3(2): 41-53. doi: 10.3934/bdia.2018006 Research article

Export file:

Format

RIS(for EndNote,Reference Manager,ProCite)
BibTex
Text

Content

Citation Only
Citation and Abstract

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

David E. Bernholdt, Mark R. Ciancosa, David L. Green, Kody J.H. Law, Alexander Litvinenko, Jin M. Park

1 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA
2 Fusion Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA
3 School of Mathematics, University of Manchester, UK
4 Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
5 General Atomics, San Diego, CA, USA

Received: , Accepted: , Published:

Abstract Full Text(HTML) Figure/Table

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.

Figure/Table

Supplementary

Article Metrics

References

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.

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.

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.

13.Staebler GM, Kinsey JE, Waltz RE (2007) A theory-based transport model with comprehensive physics. Phys Plasmas 14: 055909.

Download full text in PDF

Export Citation

Article outline

Show full outline