energy

Truncate the subspace based on eigenvalue energy

Specification

  • Alias: None

  • Arguments: None

Child Keywords:

Required/Optional

Description of Group

Dakota Keyword

Dakota Keyword Description

Optional

truncation_tolerance

Specify the maximum percentage (as a decimal) of the eigenvalue energy not captured by the active subspace representation.

Description

Uses a criterion based on the derivative matrix eigenvalue energy.

Usage Tips

This subspace truncation method may work best when working with non-normally distributed uncertain variables. If this automated diagnostic does not yield desirable results, consider using the explicit model-active_subspace-dimension truncation option or one of the other truncation methods.

Theory

Using the eigenvalue energy truncation metric, the subspace size is determined using the following equation:

\[n = \inf \left\lbrace d \in \mathbf{Z} \quad\middle|\quad 1 \le d \le N \quad \wedge\quad 1 - \frac{\sum_{i = 1}^{d} \lambda_i}{\sum_{i = 1}^{N} \lambda_i} \,<\, \epsilon \right\rbrace\]

where \(\epsilon\) is the model-active_subspace-truncation_method-energy-truncation_tolerance, \(n\) is the estimated subspace size, \(N\) is the size of the full space, and \(\lambda_i\) are the eigenvalues of the derivative matrix.