Nonhierarchical multi-model fusion using spatial random processes

Shishi Chen, Zhen Jiang, Shuxing Yang, Daniel W. Apley, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


New model fusion techniques based on spatial-random-process modeling are developed in this work for combining multi-fidelity data from simulations and experiments. Existing works in multi-fidelity modeling generally assume a hierarchical structure in which the levels of fidelity of the simulation models can be clearly ranked. In contrast, we consider the nonhierarchical situation in which one wishes to incorporate multiple models whose levels of fidelity are unknown or cannot be differentiated (e.g., if the fidelity of the models changes over the input domain). We propose three new nonhierarchical multi-model fusion approaches with different assumptions or structures regarding the relationships between the simulation models and physical observations. One approach models the true response as a weighted sum of the multiple simulation models and a single discrepancy function. The other two approaches model the true response as the sum of one simulation model and a corresponding discrepancy function, and differ in their assumptions regarding the statistical behavior of the discrepancy functions, such as independence with the true response or a common spatial correlation function. The proposed approaches are compared via numerical examples and a real engineering application. Furthermore, the effectiveness and relative merits of the different approaches are discussed.

Original languageEnglish (US)
Pages (from-to)503-526
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
StatePublished - May 18 2016


  • Computer experiments
  • Multi-fidelity modeling
  • Multi-model fusion
  • Nonhierarchical model fidelity
  • Spatial random process

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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