Optimization of Nonanalog Monte Carlo Games Using Differential Operator Sampling

The amounts of change in the variance and in the efficiency of nonanalog Monte Carlo simulations for certain variations in the biasing parameters are important quantities when optimizing such simulations. Anew approach, based on the differential operator sampling technique, is outlined to estimate t...

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Vydané v:Nuclear science and engineering Ročník 124; číslo 2; s. 291 - 308
Hlavní autori: Sarkar, P. K., Rief, Herbert
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: La Grange Park, IL Taylor & Francis 01.10.1996
American Nuclear Society
Predmet:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Monte carlo and statistical methods
Neutron physics
Neutron transport: diffusion and moderation
Nuclear engineering and nuclear power studies
Nuclear physics
Numerical approximation and analysis
Numerical optimization
Physics
Monte Carlo method
Algorithms
Sampling theory
Random walk
Differential operator
Computerized simulation
Optimization
Neutron transport
ISSN:0029-5639, 1943-748X
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Abstract The amounts of change in the variance and in the efficiency of nonanalog Monte Carlo simulations for certain variations in the biasing parameters are important quantities when optimizing such simulations. Anew approach, based on the differential operator sampling technique, is outlined to estimate the derivatives of variance and efficiency with respect to the biasing parameters; the same simulation constructed to solve the primary problem is used. An algorithm requiring the first- and higher order derivatives of the natural logarithm of the second moment to predict minimum-variance-biasing parameters is presented. Equations pertaining to the algorithm are derived and solved numerically for an exponentially transformed one-group slab transmission problem for various slab thicknesses and scattering probabilities. The results indicate that optimization of nonanalog simulations can be achieved so that the present method will be useful in self-learning Monte Carlo schemes.
AbstractList The amounts of change in the variance and in the efficiency of nonanalog Monte Carlo simulations for certain variations in the biasing parameters are important quantities when optimizing such simulations. Anew approach, based on the differential operator sampling technique, is outlined to estimate the derivatives of variance and efficiency with respect to the biasing parameters; the same simulation constructed to solve the primary problem is used. An algorithm requiring the first- and higher order derivatives of the natural logarithm of the second moment to predict minimum-variance-biasing parameters is presented. Equations pertaining to the algorithm are derived and solved numerically for an exponentially transformed one-group slab transmission problem for various slab thicknesses and scattering probabilities. The results indicate that optimization of nonanalog simulations can be achieved so that the present method will be useful in self-learning Monte Carlo schemes.
Author Rief, Herbert
Sarkar, P. K.
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crossref_primary_10_1006_jcph_1998_6039
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Issue 2
Keywords Monte Carlo method
Algorithms
Sampling theory
Random walk
Differential operator
Computerized simulation
Optimization
Neutron transport
Language English
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SubjectTerms Computational techniques
Exact sciences and technology
Mathematical methods in physics
Monte carlo and statistical methods
Neutron physics
Neutron transport: diffusion and moderation
Nuclear engineering and nuclear power studies
Nuclear physics
Numerical approximation and analysis
Numerical optimization
Physics
Title Optimization of Nonanalog Monte Carlo Games Using Differential Operator Sampling
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