Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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hierarchical


Hierarchical approximations use corrected results from a low fidelity model as an approximation to the results of a high fidelity "truth" model.

Specification

Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required ordered_model_fidelities

Specification of an hierarchy of model fidelities, ordered from low to high.

Required correction Correction approaches for surrogate models

Description

Hierarchical approximations use corrected results from a low fidelity model as an approximation to the results of a high fidelity "truth" model. These approximations are also known as model hierarchy, multifidelity, variable fidelity, and variable complexity approximations. The required ordered_model_fidelities specification points to a sequence of model specifications of varying fidelity, ordered from lowest to highest fidelity. The highest fidelity model provides the truth model, and each of the lower fidelity alternatives provides different levels of approximation at different levels of cost.

In multifidelity optimization, the search algorithm relies primarily on the lower fidelity models, which are corrected for consistency with higher fidelity models. The higher fidelity models are used primarily for verifying candidate steps based on solution of low fidelity approximate subproblems and updating for low fidelity corrections. In multifidelity uncertainty quantification, resolution levels are tailored across the ordered model hierarchy with fine resolution of the lowest fidelity and then decreasing resolution for each level of model discrepancy.

The correction specification specifies which correction technique will be applied to the low fidelity results in order to match the high fidelity results at one or more points. In the hierarchical case (as compared to the global case), the correction specification is required, since the omission of a correction technique would effectively eliminate the purpose of the high fidelity model. If it is desired to use a low fidelity model without corrections, then a hierarchical approximation is not needed and a single model should be used. Refer to global for additional information on available correction approaches.

Theory

Multifidelity Surrogates : Multifidelity modeling involves the use of a low-fidelity physics-based model as a surrogate for the original high-fidelity model. The low-fidelity model typically involves a coarser mesh, looser convergence tolerances, reduced element order, or omitted physics. It is a separate model in its own right and does not require data from the high-fidelity model for construction. Rather, the primary need for high-fidelity evaluations is for defining correction functions that are applied to the low-fidelity results.

Multifidelity Surrogate Models

A second type of surrogate is the {model hierarchy} type (also called multifidelity, variable fidelity, variable complexity, etc.). In this case, a model that is still physics-based but is of lower fidelity (e.g., coarser discretization, reduced element order, looser convergence tolerances, omitted physics) is used as the surrogate in place of the high-fidelity model. For example, an inviscid, incompressible Euler CFD model on a coarse discretization could be used as a low-fidelity surrogate for a high-fidelity Navier-Stokes model on a fine discretization.

See Also

These keywords may also be of interest: