Adaptive sparse polynomial dimensional decomposition for derivative-based sensitivity

Kunkun Tang, Jonathan M. Wang, Jonathan B. Freund

Research output: Contribution to journalArticlepeer-review


For applications, such as the plasma-coupled combustion system we consider, derivative-based sensitivity indices (DSI) are known to have several advantages over Sobol's total sensitivity indices, especially for small sample sizes. Several properties of derivative-based sensitivity measures are leveraged to develop a new and efficient numerical approach to estimate them. It is based on computing the DSI measures by effectively cost-free Monte Carlo sampling of an adaptively constructed orthogonal polynomial surrogate with uncertain input parameters that can have arbitrary probability distributions. The adaptivity reduces the number of necessary model evaluations, which is demonstrated both in a constructed example (the Moon function) and in two plasma-combustion systems with up to 55 uncertain parameters. Unimportant parameters are successfully identified and neglected with a low number of model evaluations, which makes it an attractive non-intrusive approach when adjoint solutions are unavailable to provide sensitivity information.

Original languageEnglish (US)
Pages (from-to)303-321
Number of pages19
JournalJournal of Computational Physics
StatePublished - Aug 15 2019


  • Derivative-based sensitivity indices
  • Global sensitivity analysis
  • High dimensionality
  • Non-intrusive sensitivity
  • Polynomial dimensional decomposition (PDD)

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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