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 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.