TY - JOUR

T1 - Regularized random-sampling high dimensional model representation (RS-HDMR)

AU - Li, Genyuan

AU - Rabitz, Herschel Albert

AU - Hu, Jishan

AU - Chen, Zheng

AU - Ju, Yiguang

N1 - Funding Information:
This work was supported by the STTR program of the Department of Defense. Support for this work has also been provided partially by the USEPA through the Environmental Bioinformatics and Computational Toxicology Center (ebCTC), under STAR grant number GAD R 832721-010.

PY - 2008/3

Y1 - 2008/3

N2 - High Dimensional Model Representation (HDMR) is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior. HDMR is based on a hierarchy of component functions of increasing dimensions. The Random-Sampling High Dimensional Model Representation (RS-HDMR) is a practical approach to HDMR utilizing random sampling of the input variables. To reduce the sampling effort, the RS-HDMR component functions are approximated in terms of a suitable set of basis functions, for instance, orthonormal polynomials. Oscillation of the outcome from the resultant orthonormal polynomial expansion can occur producing interpolation error, especially on the input domain boundary, when the sample size is not large. To reduce this error, a regularization method is introduced. After regularization, the resultant RS-HDMR component functions are smoother and have better prediction accuracy, especially for small sample sizes (e.g., often few hundred). The ignition time of a homogeneous H2/air combustion system within the range of initial temperature, 1000 < T 0 < 1500 K, pressure, 0.1 < P < 100 atm and equivalence ratio of H 2/O2, 0.2 < R < 10 is used for testing the regularized RS-HDMR.

AB - High Dimensional Model Representation (HDMR) is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior. HDMR is based on a hierarchy of component functions of increasing dimensions. The Random-Sampling High Dimensional Model Representation (RS-HDMR) is a practical approach to HDMR utilizing random sampling of the input variables. To reduce the sampling effort, the RS-HDMR component functions are approximated in terms of a suitable set of basis functions, for instance, orthonormal polynomials. Oscillation of the outcome from the resultant orthonormal polynomial expansion can occur producing interpolation error, especially on the input domain boundary, when the sample size is not large. To reduce this error, a regularization method is introduced. After regularization, the resultant RS-HDMR component functions are smoother and have better prediction accuracy, especially for small sample sizes (e.g., often few hundred). The ignition time of a homogeneous H2/air combustion system within the range of initial temperature, 1000 < T 0 < 1500 K, pressure, 0.1 < P < 100 atm and equivalence ratio of H 2/O2, 0.2 < R < 10 is used for testing the regularized RS-HDMR.

KW - Combustion

KW - High dimensional model representation (HDMR)

KW - Ignition

KW - Orthonormal polynomials

KW - Regularization

KW - Smoothing

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U2 - 10.1007/s10910-007-9250-x

DO - 10.1007/s10910-007-9250-x

M3 - Article

AN - SCOPUS:43249103947

SN - 0259-9791

VL - 43

SP - 1207

EP - 1232

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 3

ER -