Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks

Conference · Fri Mar 23 04:00:00 EST 2001

OSTI ID:15005484

Brantley, P S

An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S{sub N}) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems.

• Research Organization: Lawrence Livermore National Lab., CA (US)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 15005484
• Report Number(s): UCRL-JC-143205
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
DISCRETE ORDINATE METHOD
MINIMIZATION
NEURAL NETWORKS
SLABS