Random Sampling-High Dimensional Model Representation (RS-HDMR) and orthogonality of its different order component functions

Journal of Physical Chemistry A

Volumn 110, Issue 7, 2006, Pages 2474-2485

  Li, Genyuan ^a   Hu, Jishan ^b   Wang, Sheng Wei ^c   Georgopoulos, Panos G ^c   Schoendorf, Jacqueline ^d   Rabitz, Herschel ^a  

^a PRINCETON UNIVERSITY   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c RUTGERS UNIVERSITY   (United States)

^d NORTHROP GRUMMAN CORPORATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HDMR COMPONENT FUNCTIONS; RANDOM SAMPLING-HIGH DIMENSIONAL MODEL;

APPROXIMATION THEORY; CARRIER CONCENTRATION; ELECTRONS; FUNCTIONS; POLYNOMIALS;

MATHEMATICAL MODELS;

IONOPHORE;

ALGORITHM; ARTICLE; CHEMISTRY; ELECTRON; KINETICS; THEORETICAL MODEL;

ALGORITHMS; ELECTRONS; IONOPHORES; KINETICS; MODELS, THEORETICAL;

EID: 33644918017     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp054148m     Document Type: Article

References (24)

1. Rabitz, H.; Alis, O. F.; Shorter, J.; Shim, K. Efficient input-output model representations. Comput. Phys. Commun. 1999, 117, 11-20.
2. 1-β-γ alloys. Phys. Rev. B 1998, 55, 1940-1946.
3. Aus, O. F.; Rabitz, H. General foundations of high dimensional model representations. J. Math. Chem. 1999, 25, 197-233.
4. Shorter, J.; Rabitz, H. An efficient chemical kinetics solver using high dimensional model representations. J. Phys. Chem. A 1999, 103, 7192-7198.
5. Alis, O. F.; Rabitz, H. Efficient implementation of high dimensional model representations. J. Math. Chem. 2001, 29, 127-142.
6. Li, G.; Rosenthal, C.; Rabitz, H. High dimensional model representations. J. Phys. Chem. A 2001, 105, 7765-7777.
7. Wang, S. W.; Levy, H., II; Li, G.; Rabitz, H. Fully equivalent operational models for atmospheric chemical kinetics within global chemistry-transport models. J. Geophys. Res. 1999, 104 (No. D23), 30417-30426.
8. Shorter, J.; Rabitz, H. Radiation transport simulation by means of a fully equivalent operational model. Geophys. Res. Lett. 2000, 27, 3485-3488.
9. Li, G.; Wang, S. W.; Rabitz, H. Practical approaches to construct RS-HDMR component functions. J. Phys. Chem. 2002, 106, 8721-8733.
10. Li, G.; Wang, S. W.; Rabitz, H.; Wang, S. K.; Jáffe, P. Global uncertainty assessments of a mathematical model for trace metal bioremediation. Chem. Eng. Sci. 2002, 57, 4445-4460.
11. Wang, S. W.; Georgopoulos, P. G.; Li, G.; Rabitz, H. Random sampling-high dimensional model representation (RS-HDMR) with non-uniformly distributed variables: application to an integrated multimedia/multipathway exposure and dose model for trichloroethylene. J. Phys. Chem. A 2003, 107, 4707-4718.
12. Li, G.; Wang, S. W.; Rosenthal, C.; Rabitz, H. High dimensional model representations generated from low dimensional data samples, I. mp-Cut-HDMR. J. Math. Chem. 2001, 30, 1-30.
13. Li, G.; Artamonov, M.; Rabitz, H.; Wang, S. W.; Georgopoulos, P. G.; Demiralp, M. High dimensional model representations generated from low order terms - lp-RS-HDMR. J. Comput. Chem. 2003, 24, 647-656.
14. Li, G.; Rabitz, H.; Wang, S. W.; Georgopoulos, P. G. Correlation method for variance reduction of Monte Carlo integration in RS-HDMR. J. Comput. Chem. 2003, 24, 277-283.
15. Li, G.; Rabitz, H. Ratio control variate method for variance reduction of Monte Carlo integration in RS-HDMR. J. Comput. Chem., in press.
16. Takemura, A., Tensor analysis of ANOVA decomposition. J. Am. Statist. Assoc. 1983, 78, 894-900.
17. Sobol, I. M. Sensitivity Estimates for Nonlinear Mathematical Models. Mathematical Modeling and Computational Experiments 1993, 1, 407-414.
18. Geremia, J. M.; Rabitz, H.; Rosenthal, C. Constructing global functional maps between molecular potentials and quantum observables. J. Chem. Phys. 2001, 114, 9325-9336.
19. Li, G.; Rabitz, H.; Wang, S. W.; Georgopoulos, P. G. Characterizing uncertainties in human exposure modeling through the random sampling-high dimensional model representation (RS-HDMR) Methodology. IJRAM 2005, 5, 387-406.
20. Feng, X. J.; Hooshangi, S.; Chen, D.; Li, G.; Weiss, R.; Rabitz, H. Optimizing genetic Circuits by global sensitivity analysis. Biophys. J. 2004, 87, 2195-2202.
21. Larsen, R. J.; Marx, M. L. An Introduction to Probability and its Application; Prentice-Hall: Englewood Cliffs, New Jersey, 1985.
22. Evan, M.; Swartz, T. Approximating Integrals via Monte Carlo and Deterministic Methods; Oxford University Press: Oxford, NY, 2000.
23. Risk assessment toxicity values in the Risk Assessment Information System (RAIS) database (http://rais.ornl.gov/tox/profiles/trichloroethene_r-agsa. shtml). Oak Ridge National Laboratory: Oak Ridge, TN, 2004.
24. Deutsch, F. Best Approximation in Inner Product Space; Springer: New York, 2001.