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Correlation method for variance reduction of Monte Carlo integration in RS-HDMR
Genyuan Li1, Herschel Rabitz, Sheng-Wei Wang
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Journal of Computational Chemistry
|January 28, 2003
Summary
This study introduces a correlation method to improve the accuracy of Random Sampling-High Dimensional Model Representation (RS-HDMR) expansions. The new technique significantly reduces errors in Monte Carlo integration for more efficient function representation.
Area of Science:
- Computational Mathematics
- Numerical Analysis
Background:
- High Dimensional Model Representation (HDMR) offers efficient methods for representing complex, high-dimensional functions.
- Random Sampling-HDMR (RS-HDMR) utilizes random sampling and polynomial expansions, with accuracy dependent on Monte Carlo integration.
Purpose of the Study:
- To enhance the accuracy of RS-HDMR expansions by reducing Monte Carlo integration errors.
- To develop a more efficient method for determining expansion coefficients in RS-HDMR.
Main Methods:
- Implementation of a correlation method to minimize Monte Carlo integration error.
- An iterative procedure for determining RS-HDMR expansion coefficients using the correlation method.
Main Results:
- The correlation method significantly improves the accuracy of RS-HDMR expansions compared to direct Monte Carlo integration.
- Achieved comparable accuracy with hundreds of samples to thousands of samples using direct Monte Carlo integration in a four-dimensional test case.
Conclusions:
- The correlation method provides a substantial improvement in the accuracy and efficiency of RS-HDMR.
- This enhanced RS-HDMR technique is effective for representing high-dimensional functions with fewer samples.