Solutions of Special Forms of the Neutron Transport Equation Using Neural Networks




Conference paper

Conference title

Arab Atomic Energy Agency


Wajdi Mohamed Ratemi
Essam S. AL- Sagear


109 - 127


The neutron transport equation represents the description of the neutron flux in nuclear reactors as a function of seven independent variables. Three of these are spatial (X, Y, Z), one for the neutron energy (E), and two for the neutron direction (theta,phi),and one for the time (t). This complicated dependence makes the analytical solution of the neutron transport equation a quite tedious job, and almost impossible even with the use of highly sophisticated computers. This resulted in many simplification for the purpose of its solution. In this study, the neural network concept has been adopted for tackling such problem in stages. In Neural network there is no need to know the physical principles of the system, neither it necessitates the linearity of the system to be analyzed, and furthermore, the network has the capability of generalization. Special forms of the neutron transport equation have been used as reference models to train the different neural network architectures.Such reference model are; the time independent one group diffusion equation in one dimensional, and three dimensional cases, and multi-energy two dimensional diffusion equation, and finally the second order even parity form of the neutron transport equation. After the appropriate training of the designed networks, such networks were able to predict the flux behavior at neutron fluxes without the use of complicated computer codes, and this can be a valuable tool for decision support systems used by nuclear reactor operators.  



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