Adaptively Learning an Importance Function Using Transport Constrained Monte Carlo
It is well known that a Monte Carlo estimate can be obtained with zero-variance if an exact importance function for the estimate is known. There are many ways that one might iteratively seek to obtain an ever more exact importance function. This paper describes a method that has obtained ever more exact importance functions that empirically produce an error that is dropping exponentially with computer time. The method described herein constrains the importance function to satisfy the (adjoint) Boltzmann transport equation. This constraint is provided by using the known form of the solution, usually referred to as the Case eigenfunction solution.
Unable to display preview. Download preview PDF.
- 2.Zero-Variance Solutions for Linear Monte Carlo, Thomas E. Booth, Nuclear Science and Engineering: 102, 332–340 (1989)Google Scholar
- 3.Exponential Convergence on a Continuous Monte Carlo Transport Problem Thomas E. Booth Nuclear Science and Engineering: vol. 127, No. 3, p338 (1997)Google Scholar
- 4.“Nuclear Reactor Theory,” George I. Bell and Samuel Glasstone, Van Nostrand Reinhold Company, Copyright 1970 by Litton Educational PublishingGoogle Scholar
- 5.Monte Carlo Estimates of Transport Solutions to the Isotropic Slab Thomas E. Booth, Nuclear Science and Engineering: vol 130 Nov. 1998Google Scholar
- 6.“Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables”, edited by Milton Abramowitz and Irene Stegun, National Bureau of Standards Applied Mathematics Series 55, June 1964Google Scholar
- 7.J. Spanier, “Geometrically Convergent Learning Algorithms for for Global Solutions of Transport Problems,” Proceedings of the Third International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, June 22–26, 1998, Claremont CaliforniaGoogle Scholar