High-Dimensional Model Representations

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. [Pg.108]

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... [Pg.123]

Rabitz H, Alis OF (1999) General foundations of high-dimensional model representations. J Math Chem 25 197... [Pg.143]

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... [Pg.143]

Manzhos S, Carrington T (2006) A random-sampling high dimensional model representation neural network for building potential eneigy surfaces. J Chem Phys 125 084109... [Pg.143]

Chen, S., Brune, W.H., Oluwole, O.O., Kolb, C.E., Bacon, F., Li, G.Y., Rabitz, H. Global sensitivity analysis of the regional atmospheric chemical mechanism an application of random sampling-high dimensional model representation to urban oxidation chemistry. Environ. Sci. Technol. 46, 11162-11170 (2012)... [Pg.135]

Fell, B., Kucherenko, S., Shah, N., IEEE Comparison of Monte Carlo and Quasi Monte Carlo sampling methods in high dimensional model representation. SIMUL 2009 First International Conference on Advances in System Simulation. IEEE, New York (2009)... [Pg.136]

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)... [Pg.138]

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)... [Pg.143]

Ziehn, T., Tomlin, A.S. Global sensitivity analysis of a 3D street canyon model - part I the development of high dimensional model representations. Atm. Environ. 42, 1857-1873 (2008a)... [Pg.144]

Shorter, J.A., Ip, P.C., Rabitz, H.A. An efficient chemical kinetics solver using high dimensional model representation. J. Phys. Chem. A 103, 7192-7198 (1999)... [Pg.308]

Rao BN, Chowdhury R (2009) Enhanced high dimensional model representation for reUability analysis. Int J Numer Methods Eng 77(5) 719-750 Richard RM (1993) PRCONN manual. RMR Design Group, Tucson... [Pg.3642]

Sobol IM (2003) Theorems and examples on high dimensional model representations. Reliab Eng Syst Saf 79(2) 187-193... [Pg.3642]

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