Correlation method for variance reduction of Monte Carlo integration in RS-HDMR |
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Authors: | Li Genyuan Rabitz Herschel Wang Sheng-Wei Georgopoulos Panos G |
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Affiliation: | Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. |
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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. |
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Keywords: | HDMR high dimensional systems random sampling correlation method with Monte Carlo integration atmospheric chemistry |
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