Global uncertainty assessments by high dimensional model representations (HDMR)

Li, Genyuan; Wang, Sheng Wei; Rabitz, Herschel; Wang, Sookyun; Jaffé, Peter R.

doi:10.1016/s0009-2509(02)00417-7

Cited by 163 publications

(109 citation statements)

References 18 publications

Supporting

Mentioning

109

Contrasting

Order By: Relevance

“…HDMR is another variance-based method, which was introduced for improving the analysis of the input -output behaviour in high-dimensional systems [65,66]. The HDMR method has been applied to the global sensitivity and uncertainty analysis of the mathematical models.…”

Section: Random Sampling High-dimensional Model Representation (Rs-hdmr)mentioning

confidence: 99%

“…Previous work indicates that HDMR expansions to the second order can provide a satisfactory description of the model output for many systems [65,67]. The sensitivity analysis method by RS-HDMR is based on the RS-HDMR component functions, which have the following forms…”

Section: Random Sampling High-dimensional Model Representation (Rs-hdmr)mentioning

confidence: 99%

“…For RS-HDMR component functions, the model input x i is rescaled such that 0 ≤ x i ≤ 1. Using the orthogonality of the component functions, RS-HDMR defines the total variance s 2 [47,65] …”

Section: Random Sampling High-dimensional Model Representation (Rs-hdmr)mentioning

confidence: 99%

See 2 more Smart Citations

Sensitivity analysis approaches applied to systems biology models

2011

IET Systems Biology

330

263

View full text Add to dashboard Cite

With the rising application of systems biology, sensitivity analysis methods have been widely applied to study the biological systems, including metabolic networks, signalling pathways and genetic circuits. Sensitivity analysis can provide valuable insights about how robust the biological responses are with respect to the changes of biological parameters and which model inputs are the key factors that affect the model outputs. In addition, sensitivity analysis is valuable for guiding experimental analysis, model reduction and parameter estimation. Local and global sensitivity analysis approaches are the two types of sensitivity analysis that are commonly applied in systems biology. Local sensitivity analysis is a classic method that studies the impact of small perturbations on the model outputs. On the other hand, global sensitivity analysis approaches have been applied to understand how the model outputs are affected by large variations of the model input parameters. In this review, the author introduces the basic concepts of sensitivity analysis approaches applied to systems biology models. Moreover, the author discusses the advantages and disadvantages of different sensitivity analysis methods, how to choose a proper sensitivity analysis approach, the available sensitivity analysis tools for systems biology models and the caveats in the interpretation of sensitivity analysis results.

show abstract

Section: Random Sampling High-dimensional Model Representation (Rs-hdmr)mentioning

confidence: 99%

Section: Random Sampling High-dimensional Model Representation (Rs-hdmr)mentioning

confidence: 99%

See 1 more Smart Citation

Sensitivity analysis approaches applied to systems biology models

2011

IET Systems Biology

330

263

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…The partial variances D i and D ij for sensitivity analysis purposes are easily calculated from the HDMR component functions (Li, G. et al, 2002b). Once the partial variances are determined sensitivity indices can be calculated as follows:…”

Section: Global Sensitivity Analyisis Using Hdmrmentioning

confidence: 99%

The effects of parametric uncertainties in simulations of a reactive plume using a Lagrangian stochastic model

Ziehn

Dixon

Tomlin

2009

Atmospheric Environment

View full text Add to dashboard Cite

Abstract:A combined Lagrangian stochastic model with micro mixing and chemical sub-models is used to investigate a reactive plume of nitrogen oxides (NO x ) released into a turbulent grid flow doped with ozone (O 3 ). Sensitivities to the model input parameters are explored for high NO x model scenarios. A wind tunnel experiment is used to provide the simulation conditions for the first case study where photolysis reactions are not included and the main uncertainties occur in the parameters defining the turbulence scales, the source size and the reaction rate of NO (nitric oxide) with O 3 . Using nominal values of the parameters from previous studies, the model gives a good representation of the radial profile of the conserved scalar [NO x ] compared to the experiments, although the width of the simulated profile is slightly smaller, especially at longer distances from the source. For this scenario, the Lagrangian velocity structure function coefficient has the largest impact on simulated [NO x ] profiles. At the next stage photolysis reactions are included in a chemical scheme consisting of eight reactions between species NO, O, O 3 and NO 2 . The high dimensional model representation (HMDR) method is used to investigate the effects of uncertainties in the various model inputs resulting from the parameterisation of important physical and chemical processes in the reactive plume model, on the simulation of primary and secondary chemical species concentrations. Both independent and interactive effects of the parameters are studied. In total 22 parameters are assumed to be uncertain, among them the turbulence parameters, temperature dependant rate parameters, photolysis rates, temperature, fraction of NO in total NO x at the source and background concentration of O 3 . Only uncertainties in the mixing time scale coefficient and the structure function coefficient are responsible for the variance in the [NO x ] radial profile. On the other hand, the variance in the [O 3 ] profile is caused by parameters describing both physical and chemical processes.

show abstract

Global uncertainty assessments by high dimensional model representations (HDMR)

Cited by 163 publications

References 18 publications

Sensitivity analysis approaches applied to systems biology models

Sensitivity analysis approaches applied to systems biology models

Variance-based interaction index measuring heteroscedasticity

The effects of parametric uncertainties in simulations of a reactive plume using a Lagrangian stochastic model

Contact Info

Product

Resources

About