Journal of Scientific Computing

, Volume 79, Issue 2, pp 1335–1359 | Cite as

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

  • Manav Vohra
  • Alen Alexanderian
  • Cosmin Safta
  • Sankaran MahadevanEmail author


Surrogate modeling has become a critical component of scientific computing in situations involving expensive model evaluations. However, training a surrogate model can be remarkably challenging and even computationally prohibitive in the case of intensive simulations and large-dimensional systems. We develop a systematic approach for surrogate model construction in reduced input parameter spaces. A sparse set of model evaluations in the original input space is used to approximate derivative based global sensitivity measures (DGSMs) for individual uncertain inputs of the model. An iterative screening procedure is developed that exploits DGSM estimates in order to identify the unimportant inputs. The screening procedure forms an integral part of an overall framework for adaptive construction of a surrogate in the reduced space. The framework is tested for computational efficiency through an initial implementation in simple test cases such as the classic Borehole function, and a semilinear elliptic PDE with a random source function. The framework is then deployed for a realistic application from chemical kinetics, where we study the ignition delay in an \(\hbox {H}_2{/}\hbox {O}_2\) reaction mechanism with 19 and 33 uncertain rate-controlling parameters. It is observed that significant computational gains can be attained by constructing accurate low-dimensional surrogates using the proposed framework.


Global sensitivity analysis Polynomial chaos Parameter screening Surrogate modeling 



M. Vohra and S. Mahadevan gratefully acknowledge funding support from the National Science Foundation (Grant No. 1404823, CDSE Program). C. Safta was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, as part of the Computational Chemical Sciences Program. The research of A. Alexanderian was partially supported by the National Science Foundation through the Grant DMS-1745654. M. Vohra would also like to sincerely thank Dr. Xun Huan at Sandia National Labs for his guidance pertaining to the usage of TChem for the chemical kinetics application in this work. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department Of Energy or the United States Government.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringVanderbilt UniversityNashvilleUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Sandia National LaboratoriesLivermoreUSA

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