Correlation method for variance reduction of Monte Carlo integration in RS-HDMR.
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.
Li
Genyuan
G
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Rabitz
Herschel
H
Wang
Sheng-Wei
SW
Georgopoulos
Panos G
PG