SOBOLHDMR: A General-Purpose Modeling Software

  • Sergei Kucherenko
Part of the Methods in Molecular Biology book series (MIMB, volume 1073)


One of the dominant approaches in synthetic biology is the development and implementation of minimal circuits that generate reproducible and controllable system behavior. However, most biological systems are highly complicated and the design of sustainable minimal circuits can be challenging. SobolHDMR is a general-purpose metamodeling software that can be used to reduce the complexity of mathematical models, such as those for metabolic networks and other biological pathways, yielding simpler descriptions that retain the features of the original model. These descriptions can be used as the basis for the design of minimal circuits or artificial networks.

Key words

Model reduction Global sensitivity analysis Metamodeling Software 


  1. 1.
    Saltelli A, Ratto M et al (2008) A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Wiley, West SussexGoogle Scholar
  2. 2.
    Sathyanarayanamurthy H, Chinnam RB (2009) Metamodels for variable importance decomposition with applications to probabilistic engineering design. Comput Ind Eng 57:996–1007CrossRefGoogle Scholar
  3. 3.
    Kucherenko S, Fernandez MR, Pantelide C, Shah N (2009) Monte Carlo Evaluation of derivative-based global sensitivity measures. Reliab Eng Syst Saf 94:1135–1148CrossRefGoogle Scholar
  4. 4.
    Rabitz H, Alis OF et al (1999) Efficient input–output model representations. Comput Phys Commun 117:11–20CrossRefGoogle Scholar
  5. 5.
    Li G, Wang S, Rabitz H (2002) Practical approaches to construct RS-HDMR component functions. J Phys Chem 106:8721–8733CrossRefGoogle Scholar
  6. 6.
    Li G, Wang S et al (2002) Global uncertainty assessment by high dimensional model representation (HDMR). Chem Eng Sci 57:4445–4460CrossRefGoogle Scholar
  7. 7.
    Li ZQ, Xiao YG, Li ZMS (2006) Modeling of multi-junction solar cells by Crosslight APSYS. Accessed 18 June 2010
  8. 8.
    Feil B, Kucherenko S, Shah N (2009) Comparison of Monte Carlo and Quasi-Monte Carlo sampling methods in High Dimensional Model Representation. In: Proc First International Symposium Adv System Simulation, SIMUL 2009, Porto, Portugal, 20–25 September 2009Google Scholar
  9. 9.
    Zuniga MM, Kucherenko S, Shah N (2013) Metamodelling with independent and dependent inputs. Comput Phys Commun 184(6):1570–1580Google Scholar
  10. 10.
    Sobol’ IM, Tarantola S et al (2007) Estimating the approximate error when fixing unessential factors in global sensitivity analysis. Reliab Eng Syst Saf 92:957–960CrossRefGoogle Scholar
  11. 11.
    Sobol IM, Kucherenko S (2009) Derivative based global sensitivity measures and their link with global sensitivity indices. Math Comput Simul 79:3009–3017CrossRefGoogle Scholar
  12. 12.
    Sobol IM, Kucherenko S (2010) A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Comput Phys Commun 181:1212–1217CrossRefGoogle Scholar
  13. 13.
    Kucherenko S, Zaccheus O, Munoz ZM (2012) SobolHDMR User manual. Imperial College London, LondonGoogle Scholar
  14. 14.
    Li G, Rabitz H (2006) Ratio control variate method for efficiently determining high-dimensional model representations. J Comput Chem 27:1112–1118CrossRefGoogle Scholar
  15. 15.
    Kucherenko S, Feil B, Shah N, Mauntz W (2011) The identification of model effective dimensions using global sensitivity analysis. Reliab Eng Syst Saf 96:440–449CrossRefGoogle Scholar
  16. 16.
    Sobol’ IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Comput Simul 55:271–280CrossRefGoogle Scholar
  17. 17.
    Wang GG, Shan S (2006) Review of metamodeling techniques in support of engineering design optimization. Accessed 14 Jan 2010
  18. 18.
    Simpson TW, Peplinski JD, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17:129–150CrossRefGoogle Scholar
  19. 19.
    Wang SW, Georgopoulos PG, Li G, Rabitz H (2003) RS-HDMR with nonuniformly distributed variables: application to integrated multimedia/multipathway exposure and dose model for trichloroethylene. J Phys Chem 107:4707–4716CrossRefGoogle Scholar
  20. 20.
    Ziehn T, Tomlin AS (2008) Global sensitivity analysis of a 3D street canyon model—part I: the development of high dimensional model representations. Atmos Environ 42:1857–1873CrossRefGoogle Scholar
  21. 21.
    Sobol’ IM (2003) Theorems and examples on high dimensional model representation. Reliab Eng Syst Saf 79:187–193CrossRefGoogle Scholar
  22. 22.
    Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Safety 52:1–17CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, New York 2013

Authors and Affiliations

  • Sergei Kucherenko
    • 1
  1. 1.Department of Chemical Engineering and Chemical TechnologyImperial College LondonLondonUK

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