High-dimensional model representation HDMR

The statistical approach to chemical kinetics was developed by Li et al. (2001, 2002), and high-dimensional model representations (HDMR) were proposed as efficient tools to provide a fully global statistical analysis of a model. The work of Feng et al. (2004) was focused on how the network properties are affected by random rate constant changes. The rate constants were transformed to a logarithmic scale to ensure an even distribution over the large space. 

Li, G., Wang, S.-W., Rabitz, H., Wang, S., Jaffe, P. Global uncertainty assessments by high dimensional model representations (HDMR). Chem. Eng. Sci. 57, 4445-4460 (2002b)... 

Wang, L., Milford, J.B., Carter, W.P.L. Reactivity estimates for aromatic compounds. Part I. Uncertainty in chamber-derived parameters. Atmos. Environ. 34, 4337-4348 (2000b) Wang, S.W., Georgopoulos, P.G., Li, G., Rabitz, H. Computationally efficient atmospheric chemical kinetic modeling by means of high dimensional model representation (HDMR). Lect. Note Comput. Sci. 2179, 326-333 (2001)... 

Within the present contribution we resorted to the so-called cluster expansion (CE)[10], a variant of the n-mode representational, 22], also called highdimensional model representation or eut-high dimensional model representation (cut-HDMR)[23-26], Within the CE the potential is approximated by n-particle interaction terms. These terms are called clusters. Again the Qa refer to the composite coordinates as detailed above. The PES is approximated by the expansion... 

Li GY, Hu JS, Wang SW, Georgopoulos PG, Schoendoif J, Rabitz H (2(X)6) Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions. J Phys Chem A 110 2474—2485... 

Li, G.Y., Rabitz, H., Hu, J.S., Chen, Z., Ju, Y. Regularized random-sampling high dimensional model representation (RS-HDMR). J. Math. Chem. 43, 1207-1232 (2008b)... 

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