A geostatistical perspective for the surrogate-based integration of variable fidelity models

When constructing surrogate models, time/cost constraints make the designer frequently face the dilemma of whether to use a small sample of data obtained from, for example, high fidelity/computationally expensive computer simulations, or, a large one but with low fidelity values. More generally, variable fidelity samples can be the result of: i) different physical/mathematical representations (e.g., inviscid/Euler versus viscous/Navier–Stokes calculations), ii) alternative resolution models (e.g., fine/coarse grids), or, iii) experiments. Ideally, surrogate models should allow: a) the integration of variable fidelity samples, and, b) provide estimation and appraisal (error) information consistent with the amount and fidelity level of the available data. While there have been significant progress in this area through deterministic modeling and optimization approaches (e.g., correction surfaces, and space mapping), a spatial-stochastic perspective such as those provided by the branch of spatial statistics known as geostatistics offers distinctive advantages when satisfying the above referenced requirements (a and b). This paper discusses the effectiveness and requirements of geostatistical methods such as classic and collocated cokriging for the integration of variable fidelity models. The discussion is illustrated using well-known analytical functions and, alternative resolution models, in the surrogate-based modeling of a field scale alkali–surfactant–polymer (ASP) enhanced oil recovery (EOR) process.