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