Dakota Reference Manual: discrepancy_emulation

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discrepancy_emulation

Formulation for emulation of model discrepancies.

## Specification

Alias: none

Argument(s): none

Default: distinct

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required (Choose One) | Discrepancy Emulation Approach (Group 1) | distinct | Distinct formulation for emulation of model discrepancies.
recursive | Recursive formulation for emulation of model discrepancies.

## Description

In many uncertainty quantification approaches, model discrepancies are emulated using, e.g., polynomial chaos, stochastic collocation, or Gaussian process models. Two formulations are available for this emulation:

1. `distinct` emulation (default), in which we directly approximate the difference or ratio between the evaluations of two models or solution levels.
2. `recursive` emulation (experimental option), in which we approximate a difference or ratio among the new model evaluation and the emulator approximation of the previous model.

The latter approach is a form of hierarchical emulation in which we emulate the surplus between the previous emulator and the new modeling level. This approach has a few advantages: (i) it reduces bias by correcting for emulation errors that occur at previous levels, and (ii) it does not require paired model evaluations for each discrepancy level, which reduces cost, allows for disparate sample points, and simplifies data imports.

On the other hand, its primary disadvantage is that the aggregate emulation is only as good as its weakest link, in that a poor emulator recovery can create difficulty in accurately resolving discrepancies that are recursively dependent on it. Thus, the `distinct` approach may tend to be more expensive in exchange for greater robustness.

## Examples

    method,
            multilevel_polynomial_chaos
          expansion_order_sequence = 2
          collocation_ratio = .9
          orthogonal_matching_pursuit
          discrepancy_emulation recursive