Dakota Reference Manual: model_discrepancy

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model_discrepancy

(Experimental) Post-calibration calculation of model discrepancy correction

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | discrepancy_type | Specify the type of model discrepancy
| Optional | num_prediction_configs | Specify number of prediction locations for model discrepancy
| Optional | prediction_configs | List prediction locations for model discrepancy
| Optional | import_prediction_configs | Specify text file containing prediction configurations for model discrepancy
| Optional | export_discrepancy_file | Output file for prediction discrepancy calculations
| Optional | export_corrected_model_file | Output file for corrected model prediction calculations
| Optional | export_corrected_variance_file | Output file for prediction variance calculations

## Description

The goal of parameter calibration is to minimize the difference between experimental data, , and model observations, , where are the model parameters and is a configuration variable, such as temperature or pressure. However, it is not uncommon that, at the conclusion of parameter calibration, the agreement between experimental data and the calibrated model is not "close enough." This is often due to model form or structural error. In this case, the canonical equation

is replaced by one that also includes model discrepancy ,

In the Dakota implementation, the calculation of is performed after the model parameters are calibrated. For each observable , the discrepancy

is calculated for each value of the configuration variable, where is the optimal parameter value obtained during the calibration. For scalar responses, the model discrepancy is only a function of the configuration variables, and there is one discrepancy regression model for each observable . This set of discrepancy models may be specified to be either Gaussian process or polynomial regression models of constant, linear, or quadratic order, and each model is fit to the calculated discrepancy values. See the discrepancy_type command for more details regarding these options. For field responses, the model discrepancy is a function of the configuration variables as well as the independent field coordinates (such as time or space), and there is one discrepancy regression model for each field. In this case, the discrepancy models are Gaussian process models. The calculation of model discrepancy has not been tested for cases in which responses are mixed scalar and field responses.

The user may then specify new or "prediction" configurations at which the corrected model should be calculated, using one of the `num_prediction_configs`, `prediction_configs`, or `import_prediction_configs` keywords. If none of these keywords is specified, the number of prediction configurations is set to 10 for scalar responses. The corresponding prediction variances are also calculated, according to

Here, is the (co)variance calculated from the Gaussian process or polynomial regression model, and is the maximum variance, taken over all configuration variables for that observation. In the case of field responses, the default prediction configurations are set equal to the input configurations, and the variance information contains only the variance calculated from the Gaussian process correction model. Further details can be found in the Dakota User's and Theory Manuals.

Usage Tips

For field responses, the keyword read_field_coordinates must be specified when computing the model discrepancy. See field_calibration_terms for more information regarding options for calibration with field responses.

Expected Output

The resulting values of will be exported to the file specified using `export_discrepancy_file` or to the default file `dakota_discrepancy_tabular.dat`. The values of the corrected model at the specified prediction configurations will be exported to the file specified using `export_corrected_model_file` or to the default file `dakota_corrected_model_tabular.dat`, and the corresponding prediction variances will be exported to `dakota_discrepancy_variance_tabular.dat` or the file specified with `export_corrected_variance_file`.

## Examples

Extensive examples can be found in the Dakota User's and Theory Manuals. The input files below illustrate the options available to `model_discrepancy`

    model_discrepancy
      discrepancy_type  gaussian_process
      num_prediction_configs  11
      export_discrepancy_file  "discrepancy_values.txt"
      export_corrected_model_file  "corrected_model.txt"
      export_corrected_variance_file  "prediction_variance.txt"

    model_discrepancy
      discrepancy_type  polynomial
        correction_order  constant
      prediction_configs  1  1.5  2  2.5  3

    model_discrepancy
      discrepancy_type  polynomial
        correction_order  linear
      import_prediction_configs "prediction_configs.txt"