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

Li, Genyuan; Rabitz, Herschel; Hu, Jintao; Chen, Zheng; Ju, Yiguang

doi:10.1007/s10910-007-9250-x

Cited by 62 publications

(35 citation statements)

References 24 publications

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“…The High Dimensional Model Representation (HDMR) method is a set of tools developed by Rabitz et al [8][9][10][11][12] to capture high-dimensional input-output relationship of a complex model with a large number of input parameters. It expresses the output variable f(x) as a finite hierarchical correlated function expansion in terms of the input variables x=(x 1 , x 2 , …, x n ) in the following form [8][9][10][11][12]:…”

Section: Hdmr Methodsmentioning

confidence: 99%

“…It expresses the output variable f(x) as a finite hierarchical correlated function expansion in terms of the input variables x=(x 1 , x 2 , …, x n ) in the following form [8][9][10][11][12]:…”

Section: Hdmr Methodsmentioning

confidence: 99%

“…The last term f 1,2,…,n (x 1 , x 2 , …, x n ) reflects any residual nth-order correlated contribution of all input variables to the output f(x). Systematic optimal procedures have been developed to construct the distinct HDMR component functions in the above expansion [8][9][10][11][12]. Recently, random sampling (RS)-HDMR has been developed by Li et al [8] to accurately and efficiently treat high dimensional input-output mapping problems and has been successfully utilized in several scientific modeling applications including atmospheric chemistry [11], molecular dynamics simulations [8], and bio-kinetics modeling [13].…”

Section: Hdmr Methodsmentioning

confidence: 99%

“…These correlations [3,6,7] were obtained through curve fitting and thus the accuracy was highly constrained by the nonlinear regression process. Instead of conducting nonlinear regression, the method of High Dimensional Model Representation (HDMR, to be introduced in the next section) [8][9][10][11][12] is utilized in this paper to give more accurate correlations for the ignition delay times. Since hydrogen is widely considered as a candidate for the next-generation energy carrier, the ignition of hydrogen is important not only for combustion engines but also for safe transport and utilization of hydrogen.…”

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confidence: 99%

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Correlations for the ignition delay times of hydrogen/air mixtures

Zhao

Chen

2011

Chin. Sci. Bull.

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Correlations for the ignition delay times of hydrogen/air mixtures were developed using the method of High Dimensional Model Representation (HDMR). The hydrogen/air ignition delay times for initial conditions over a wide range of temperatures from 800 to 1600 K, pressures from 0.1 to 100 atm, and equivalence ratios from 0.2 to 10 were first calculated utilizing the full chemical mechanism. Correlations were then developed based on these ignition delay times. Two forms of correlations were constructed: the first one is an overall general model covering the whole range of the initial conditions; while the second one is a piecewise correlation model valid for initial conditions within different sub-domains. The performance of these correlations was studied through comparison with results from the full chemical mechanism as well as experimental data. It was shown that these correlations work well over the whole range of initial conditions and that the accuracy can be significantly improved by using different piecewise correlations for different sub-domains. Therefore, piecewise correlations can be used as an effective replacement for the full mechanism when the prediction of chemical time scale is needed in certain combustion modeling. Ignition delay time or reaction time [1-3] is one of the most important parameters characterizing the combustion process of different fuels and thus is very important for combustion modeling. Accurate calculation of the ignition delay time, especially for the combustion process with a variety of fuel blends in gas turbines and other combustion engines, is a complicated procedure because of the complex interaction between flows and chemical kinetics [4]. For hydrocarbon and synthetic bio-fuels with a large number of species and a broad range of time scales, enormous computation time is required to handle the detailed chemistry in reactive flow simulation [5]. Moreover, it is required to couple a full chemistry solver with a full-scale numerical flow solver which makes the whole procedure time-consuming and far beyond the limitation of current computers [3]. Therefore, there is an increasing need to find simplified alternatives which can accurately and efficiently predict the over-all behavior of all chemical reactions.*Corresponding author (email: cz@pku.edu.cn)In order to reduce the computational time due to complex chemistry, different correlations were developed to calculate the ignition delay times for different mixtures. For example, Molnar and Marek [6,7] developed reduced equations from fitted kinetics modeling for jet-A and methane fuels. More recently, Donato and Petersen [3] provided simplified correlation equations to calculate the ignition delay times of syngas/air mixtures at different initial temperatures, pressures, and equivalence ratios. These correlations [3,6,7] were obtained through curve fitting and thus the accuracy was highly constrained by the nonlinear regression process. Instead of conducting nonlinear regression, the method of High Dimensional Model Represen...

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Section: Hdmr Methodsmentioning

confidence: 99%

Section: Hdmr Methodsmentioning

confidence: 99%

Section: Hdmr Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Correlations for the ignition delay times of hydrogen/air mixtures

Zhao

Chen

2011

Chin. Sci. Bull.

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“…There are also regression methods based on HDMR [29,30,31]. The basis functions in these are polynomials.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Variance-based interaction index measuring heteroscedasticity

Ito

Couckuyt

Poles

et al. 2016

Computer Physics Communications

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This work is motivated by the need to deal with models with high-dimensional input spaces of real variables. One way to tackle high-dimensional problems is to identify interaction or non-interaction among input parameters. We propose a new variance-based sensitivity interaction index that can detect and quantify interactions among the input variables of mathematical functions and computer simulations. The computation is very similar to first-order sensitivity indices by Sobol'. The proposed interaction index can quantify the relative importance of input variables in interaction. Furthermore, detection of non-interaction for screening can be done with as low as 4n + 2 function evaluations, where n is the number of input variables. Using the interaction indices based on heteroscedasticity, the original function may be decomposed into a set of lower dimensional functions which may then be analyzed separately.

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Multiscale Integration of Toxicokinetic and Toxicodynamic Processes: From Cell and Tissue to Organ and “Whole Body” Models

Georgopoulos¹,

Isukapalli²,

Androulakis³

et al. 2009

General, Applied and Systems Toxicology

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This chapter presents a systematic summary overview of coordinated efforts taking place at the environmental bioinformatics and Computational Toxicology Center ( ebCTC.org ) towards developing a mechanistic modeling framework that integrates multiple scales of coupled toxicokinetic and toxicodynamic processes. This framework employs highly modular “whole body” computational descriptions of the human and of selected model organisms that incorporate a hierarchy of alternative formulations representing biological events in “virtual” tissues and organs. This approach allows the mechanistic consideration of multiple scales of interlinked phenomena that include molecular interactions; dynamics of intracellular biomolecular networks; spatial and stochastic aspects of cell biochemistry; integrative coupling of cellular‐level processes related to common endpoints; extracellular signaling and cell‐cell communication and interaction; aspects of functional heterogeneity in multicellular structures; dynamics of histomorphological and histopathological processes at the tissue level; and integrative coupling of processes across scales, resulting in different physiosystem phenotypes for health and disease states. The ebCTC framework offers a range of combined approaches for coupling processes and “transferring and integrating” information across multiple strata of biological organization, ranging from formal methods of multiscale analysis, including statistical descriptions of multicellular kinetics and dynamics, to simplified “top‐down” approaches, incorporating both mechanistic and phenomenological formulations that rely on point and distributional parameterizations of the finer scales. The computational implementation of the framework employs a combination of agent‐, network‐, and field‐based modeling methods. Example applications of various components of this framework are presented, spanning the range from molecular interactions to bionetwork and cellular dynamics to multiscale problems at the tissue and organ levels.

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

Cited by 62 publications

References 24 publications

Correlations for the ignition delay times of hydrogen/air mixtures

Correlations for the ignition delay times of hydrogen/air mixtures

Variance-based interaction index measuring heteroscedasticity

Multiscale Integration of Toxicokinetic and Toxicodynamic Processes: From Cell and Tissue to Organ and “Whole Body” Models

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