Correlation method for variance reduction of Monte Carlo integration in RS‐HDMR
- 9 January 2003
- journal article
- research article
- Published by Wiley in Journal of Computational Chemistry
- Vol. 24 (3), 277-283
- https://doi.org/10.1002/jcc.10172
Abstract
The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high-dimensional functions. A practical form of the technique, RS-HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS-HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS-HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS-HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 277–283, 2003Keywords
This publication has 5 references indexed in Scilit:
- Practical Approaches To Construct RS-HDMR Component FunctionsThe Journal of Physical Chemistry A, 2002
- An Efficient Chemical Kinetics Solver Using High Dimensional Model RepresentationThe Journal of Physical Chemistry A, 1999
- General foundations of high‐dimensional model representationsJournal of Mathematical Chemistry, 1999
- An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutionsComputer Physics Communications, 1998
- Monte Carlo MethodsPublished by Wiley ,1986