1Blurb:: 2Hierarchical approximations use corrected results from a low fidelity 3model as an approximation to the results of a high fidelity "truth" 4model. 5Description:: 6 7Hierarchical approximations use corrected results from a low fidelity 8model as an approximation to the results of a high fidelity "truth" 9model. These approximations are also known as model hierarchy, 10multifidelity, variable fidelity, and variable complexity 11approximations. The required \c ordered_model_fidelities specification 12points to a sequence of model specifications of varying fidelity, 13ordered from lowest to highest fidelity. 14The highest fidelity model provides the truth model, and each of the 15lower fidelity alternatives provides different levels of approximation 16at different levels of cost. 17 18In multifidelity optimization, the search algorithm relies primarily 19on the lower fidelity models, which are corrected for consistency with 20higher fidelity models. The higher fidelity models are used primarily 21for verifying candidate steps based on solution of low fidelity 22approximate subproblems and updating for low fidelity corrections. In 23multifidelity uncertainty quantification, resolution levels are 24tailored across the ordered model hierarchy with fine resolution of 25the lowest fidelity and then decreasing resolution for each level of 26model discrepancy. 27 28The \c correction specification specifies which 29correction technique will be applied to the low fidelity results in 30order to match the high fidelity results at one or more points. In the 31hierarchical case (as compared to the global case), the \c correction 32specification is required, since the omission of a correction 33technique would effectively eliminate the purpose of the high fidelity 34model. If it is desired to use a low fidelity model without 35corrections, then a hierarchical approximation is not needed and a \c 36single model should be used. Refer to \ref model-surrogate-global for 37additional information on available correction approaches. 38 39 40Topics:: 41Examples:: 42Theory:: 43 44<b> Multifidelity Surrogates </b>: Multifidelity modeling involves the 45use of a low-fidelity physics-based model as a surrogate for the 46original high-fidelity model. The low-fidelity model typically 47involves a coarser mesh, looser convergence tolerances, reduced 48element order, or omitted physics. It is a separate model in its own 49right and does not require data from the high-fidelity model for 50construction. Rather, the primary need for high-fidelity evaluations 51is for defining correction functions that are applied to the 52low-fidelity results. 53 54 55<b> Multifidelity Surrogate Models </b> 56 57A second type of surrogate is the {\em model hierarchy} type (also 58called multifidelity, variable fidelity, variable complexity, etc.). 59In this case, a model that is still physics-based but is of lower 60fidelity (e.g., coarser discretization, reduced element order, looser 61convergence tolerances, omitted physics) is used as the surrogate in 62place of the high-fidelity model. For example, an inviscid, 63incompressible Euler CFD model on a coarse discretization could be 64used as a low-fidelity surrogate for a high-fidelity Navier-Stokes 65model on a fine discretization. 66 67 68 69Faq:: 70See_Also:: model-surrogate-global, model-surrogate-local, model-surrogate-multipoint, method-multilevel_sampling, method-polynomial_chaos, method-stoch_collocation, method-surrogate_based_local 71