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Year 2022, , 726 - 738, 27.12.2022

R. Gökhan Türeci

https://doi.org/10.17776/csj.1163514
Cited By: 2

Abstract

References

  • [1] Carlson B.G., Solution of the Transport Equation by SN Approximations. Los Alamos Scientific Laboratory, LA-1599, United States, (1955) 1-29.
  • [2] Lewis E.E., Miller W.F., Computational Methods of Neutron Transport. United States, (1984).
  • [3] Case K.M., Zweifel P.F., Linear Transport Theory. Addition-Wesley: MA, (1967) 1-270.
  • [4] Case K.M., Elementary solutions of the transport equation and their applications, Annals of Phys., 9 (1) (1960) 1–23.
  • [5] Kavenoky A., The CN Method of Solving the Transport Equation: Application to Plane Geometry, Nuclear Science and Eng., 65 (2) (1978) 209-225.
  • [6] Grandjean P., Siewert C.E., The FN method in neutron-transport theory. Part II: applications and numerical results, Nucl. Sci. Eng., 69 (2) (1979) 161-168.
  • [7] Tezcan C., Kaşkaş A., Güleçyüz M.Ç., The HN method for solving linear transport equation: theory and applications, JQSRT., 78 (2) (2003) 243-254.
  • [8] Géron A., Hands-On Machine Learning with Scikit-Learn, Keras and TensorFlow, 2nd ed. O'Reilly Media, (2019).
  • [9] Chen Z., Andrejevic N., Drucker N.C., Nguyen T., Xian R.P., Smidt T., Wang Y., Ernstorfer R., Tennant D.A., Chan M., Li M., Machine learning on neutron and x-ray scattering and spectroscopies, Chem. Phys. Rev., 2 (2021) 031301.
  • [10] Whewell B., McClarren R.G., Data reduction in deterministic neutron transport calculations using machine learning, Annals of Nuclear Energy., 176 (1) (2022) 109276.
  • [11] Xie Y., Wang Y., Ma Y., Wu Z., Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary, J. Nucl. Eng., 2 (2021) 533-552.
  • [12] Zolfaghari M., Masoudi S.F., Rahmani F., Fathi A., Thermal neutron beam optimization for PGNAA applications using Q-learning algorithm and neural network, Sci. Rep., 12 (2022) 8635.
  • [13] Zheng C., Liub L., Muc L., Solving the linear transport equation by a deep neural network approach, Preprint submitted to Journal of Discrete and Continuous Dynamical System-S., 15 (4) (2021) 669-686.
  • [14] Numpy. Available at: https://numpy.org/doc/stable/user/index.html#user Retrieved August 2022.
  • [15] Scipy. Available at: https://scipy.org/ Retrieved August 2022.
  • [16] Sklearn. Available at: https://scikit-learn.org/stable/ Retrieved August 2022.
  • [17] Keras. Available at: https://keras.io/ Retrieved August 2022.
  • [18] Tensorflow. Available at: https://www.tensorflow.org/ Retrieved August 2022.
  • [19] Polyfit. Available at: https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html Retrieved August 2022.
  • [20]Sutskever, I., Vinyals O., Le Q.V., Sequence to Sequence Learning with Neural Networks, arXiv:1409.3215v3., (2014).
  • [21] Kingma D.P., Ba J.L., Adam: A Method for Stochastic Optimization, arXiv:1412.6980v9., (2017).
  • [22] Xu B., Wang N., Chen T., Li M., Empirical Evaluation of Rectified Activations in Convolution Network, arXiv:1505.00853v2., (2015).
  • [23]Clevert D., Unterthiner T., Hochreiter S., Fast and accurate deep network learning by exponential linear units (Elus), arXiv:1511.07289v5., (2016).
  • [24]Atalay M.A. The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory, Annals of Nuclear Energy., 23 (3) (1996) 183-193.

Machine Learning Applications to the One-speed Neutron Transport Problems

Year 2022, , 726 - 738, 27.12.2022

R. Gökhan Türeci

https://doi.org/10.17776/csj.1163514
Cited By: 2

Abstract

Machine learning is a branch of artificial intelligence and computer science. The purpose of machine learning is to predict new data by using the existing data. In this study, two different machine learning methods which are Polynomial Regression (PR) and Artificial Neural Network (ANN) are applied to the neutron transport problems which are albedo problem, the Milne problem, and the criticality problem. ANN applications contain two different activation functions, Leaky Relu and Elu. The training data set is calculated by using the HN method. PR and ANN results are compared with the literature data. The study is only based on the existing data; therefore, the study could be thought only data mining on the one-speed neutron transport problems for isotropic scattering. 

Keywords

Polynomial Regression Artificial Neural Network Leaky Relu activation function Elu activation functions Machine Learning

References

  • [1] Carlson B.G., Solution of the Transport Equation by SN Approximations. Los Alamos Scientific Laboratory, LA-1599, United States, (1955) 1-29.
  • [2] Lewis E.E., Miller W.F., Computational Methods of Neutron Transport. United States, (1984).
  • [3] Case K.M., Zweifel P.F., Linear Transport Theory. Addition-Wesley: MA, (1967) 1-270.
  • [4] Case K.M., Elementary solutions of the transport equation and their applications, Annals of Phys., 9 (1) (1960) 1–23.
  • [5] Kavenoky A., The CN Method of Solving the Transport Equation: Application to Plane Geometry, Nuclear Science and Eng., 65 (2) (1978) 209-225.
  • [6] Grandjean P., Siewert C.E., The FN method in neutron-transport theory. Part II: applications and numerical results, Nucl. Sci. Eng., 69 (2) (1979) 161-168.
  • [7] Tezcan C., Kaşkaş A., Güleçyüz M.Ç., The HN method for solving linear transport equation: theory and applications, JQSRT., 78 (2) (2003) 243-254.
  • [8] Géron A., Hands-On Machine Learning with Scikit-Learn, Keras and TensorFlow, 2nd ed. O'Reilly Media, (2019).
  • [9] Chen Z., Andrejevic N., Drucker N.C., Nguyen T., Xian R.P., Smidt T., Wang Y., Ernstorfer R., Tennant D.A., Chan M., Li M., Machine learning on neutron and x-ray scattering and spectroscopies, Chem. Phys. Rev., 2 (2021) 031301.
  • [10] Whewell B., McClarren R.G., Data reduction in deterministic neutron transport calculations using machine learning, Annals of Nuclear Energy., 176 (1) (2022) 109276.
  • [11] Xie Y., Wang Y., Ma Y., Wu Z., Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary, J. Nucl. Eng., 2 (2021) 533-552.
  • [12] Zolfaghari M., Masoudi S.F., Rahmani F., Fathi A., Thermal neutron beam optimization for PGNAA applications using Q-learning algorithm and neural network, Sci. Rep., 12 (2022) 8635.
  • [13] Zheng C., Liub L., Muc L., Solving the linear transport equation by a deep neural network approach, Preprint submitted to Journal of Discrete and Continuous Dynamical System-S., 15 (4) (2021) 669-686.
  • [14] Numpy. Available at: https://numpy.org/doc/stable/user/index.html#user Retrieved August 2022.
  • [15] Scipy. Available at: https://scipy.org/ Retrieved August 2022.
  • [16] Sklearn. Available at: https://scikit-learn.org/stable/ Retrieved August 2022.
  • [17] Keras. Available at: https://keras.io/ Retrieved August 2022.
  • [18] Tensorflow. Available at: https://www.tensorflow.org/ Retrieved August 2022.
  • [19] Polyfit. Available at: https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html Retrieved August 2022.
  • [20]Sutskever, I., Vinyals O., Le Q.V., Sequence to Sequence Learning with Neural Networks, arXiv:1409.3215v3., (2014).
  • [21] Kingma D.P., Ba J.L., Adam: A Method for Stochastic Optimization, arXiv:1412.6980v9., (2017).
  • [22] Xu B., Wang N., Chen T., Li M., Empirical Evaluation of Rectified Activations in Convolution Network, arXiv:1505.00853v2., (2015).
  • [23]Clevert D., Unterthiner T., Hochreiter S., Fast and accurate deep network learning by exponential linear units (Elus), arXiv:1511.07289v5., (2016).
  • [24]Atalay M.A. The critical slab problem for reflecting boundary conditions in one-speed neutron transport theory, Annals of Nuclear Energy., 23 (3) (1996) 183-193.
There are 24 citations in total.

Details

Primary Language English
Subjects Classical Physics (Other)
Journal Section Natural Sciences
Authors

R. Gökhan Türeci 0000-0001-6309-6300

Publication Date December 27, 2022
Submission Date August 17, 2022
Acceptance Date October 26, 2022
Published in Issue Year 2022

Cite

APA Türeci, R. G. (2022). Machine Learning Applications to the One-speed Neutron Transport Problems. Cumhuriyet Science Journal, 43(4), 726-738. https://doi.org/10.17776/csj.1163514

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