Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Active (variable) subspace model
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required  actual_model_pointer  Pointer to specify a fullspace model, from which to construct a lower dimensional surrogate  
Optional  initial_samples  Initial number of samples for samplingbased methods  
Optional  truncation_method  Metric that estimates active subspace size  
Optional  dimension  Explicitly specify the desired subspace size  
Optional  bootstrap_samples  Number of bootstrap replicates used in truncation metrics 
A model that transforms the original model (given by actual_model_pointer) to one with a reduced set of variables. This reduced model is identified by iteratively sampling the gradient of the original model and performing a singular value decomposition of the gradient matrix.
Expected Output
A subspace model will perform an initial sampling design to identify an active subspace using one of the truncation methods.
Usage Tips
If the desired subspace size is not identified, consider using the explicit dimension truncation option or one of the other truncation methods.
Perform an initial 100 gradient samples and use the bing_li truncation method to identify an active subspace. The truncation method uses 150 bootstrap samples to compute the Bing Li truncation metric.
model subspace id_model = 'SUBSPACE' actual_model_pointer = 'FULLSPACE' initial_samples 100 truncation_method bing_li bootstrap_samples 150
The idea behind active subspaces is to find directions in the input variable space in which the quantity of interest is nearly constant. After rotation of the input variables, this method can allow significant dimension reduction. Below is a brief summary of the process.
where has eigenvectors as columns, contains eigenvalues, and is the total number of parameters.
These eigenvectors are used to rotate the input variables.
For additional information, see: