โ Scribed by Genyuan Li; Herschel Rabitz; Sheng-Wei Wang; Panos G. Georgopoulos
No coin nor oath required. For personal study only.
The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing highโdimensional functions. A practical form of the technique, RSโHDMR, 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 RSโHDMR 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 RSโHDMR 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 RSโHDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples. ยฉ 2003 Wiley Periodicals, Inc. J Comput Chem 24: 277โ283, 2003
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