Research Article

Deep Learning Application for Milne problem with linear anisotropic scattering

Volume: 38 Number: 2 June 1, 2025
EN

Deep Learning Application for Milne problem with linear anisotropic scattering

Abstract

Using deep learning algorithms, which is a sub-branch of artificial intelligence, in this study, a deep learning model is developed according to both the number of secondary neutrons and the linear anisotropic scattering coefficient. These are independent variables that the dependent variable is the extrapolation distance. The training data set was calculated with HN method. ANN algorithm was written by TensorFlow and Keras which are the modules in Python programming language. The performance of the deep learning model for this problem has high performance so that the predicted new data which doesn’t be in the training data set is reliable according to the success of the model.

Keywords

References

  1. [1] Placzek, G., and W. Seidel., “Milne's Problem in Transport Theory”, Physical Review, 72: 550-555, (1947).
  2. [2] Noble, B., The Wiener-Hopf Technique, Pergamon Press, Oxford, (1958).
  3. [3] Case, K.M. and Zweifel, P.F., Linear Transport Theory, Massachusetts: Addition-Wesley, (1967).
  4. [4] McCormick, N.J., “One-Speed Neutron Transport Problems in Plane Geometry”, PhD thesis, The University of Michigan, (1964).
  5. [5] McCormick N. J., and Kuščer, I., “Half‐Space Neutron Transport with Linearly Anisotropic Scattering”, Journal of Mathematical Physics, 6 (12): 1939-1945, (1964).
  6. [6] Kavenoky, A., “The CN Method of Solving the Transport Equation: Application to Plane Geometry”, Nuclear Science and Engineering, 65, 209, (1978).
  7. [7] Sahni, D.C., and Kumar, V., “Numerical solution of singular integral equations of neutron transport problems”, Transport Theory and Statistical Physics, 16(7): 959-978, (1987).
  8. [8] Atalay, M. A., “Milne problem for linearly anisotropic scattering and a specularly reflecting boundary”, Annals of Nuclear Energy, 27(16): 1483-1504, (2000).

Details

Primary Language

English

Subjects

Artificial Intelligence (Other), Nuclear and Plasma Physics (Other)

Journal Section

Research Article

Early Pub Date

January 3, 2025

Publication Date

June 1, 2025

Submission Date

July 24, 2024

Acceptance Date

December 3, 2024

Published in Issue

Year 2025 Volume: 38 Number: 2

APA
Türeci, R. G. (2025). Deep Learning Application for Milne problem with linear anisotropic scattering. Gazi University Journal of Science, 38(2), 986-994. https://doi.org/10.35378/gujs.1521834
AMA
1.Türeci RG. Deep Learning Application for Milne problem with linear anisotropic scattering. Gazi University Journal of Science. 2025;38(2):986-994. doi:10.35378/gujs.1521834
Chicago
Türeci, R. Gökhan. 2025. “Deep Learning Application for Milne Problem With Linear Anisotropic Scattering”. Gazi University Journal of Science 38 (2): 986-94. https://doi.org/10.35378/gujs.1521834.
EndNote
Türeci RG (June 1, 2025) Deep Learning Application for Milne problem with linear anisotropic scattering. Gazi University Journal of Science 38 2 986–994.
IEEE
[1]R. G. Türeci, “Deep Learning Application for Milne problem with linear anisotropic scattering”, Gazi University Journal of Science, vol. 38, no. 2, pp. 986–994, June 2025, doi: 10.35378/gujs.1521834.
ISNAD
Türeci, R. Gökhan. “Deep Learning Application for Milne Problem With Linear Anisotropic Scattering”. Gazi University Journal of Science 38/2 (June 1, 2025): 986-994. https://doi.org/10.35378/gujs.1521834.
JAMA
1.Türeci RG. Deep Learning Application for Milne problem with linear anisotropic scattering. Gazi University Journal of Science. 2025;38:986–994.
MLA
Türeci, R. Gökhan. “Deep Learning Application for Milne Problem With Linear Anisotropic Scattering”. Gazi University Journal of Science, vol. 38, no. 2, June 2025, pp. 986-94, doi:10.35378/gujs.1521834.
Vancouver
1.R. Gökhan Türeci. Deep Learning Application for Milne problem with linear anisotropic scattering. Gazi University Journal of Science. 2025 Jun. 1;38(2):986-94. doi:10.35378/gujs.1521834

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