collocation_ratio

Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion.

Specification

  • Alias: None

  • Arguments: REAL

Child Keywords:

Required/Optional

Description of Group

Dakota Keyword

Dakota Keyword Description

Optional (Choose One)

Regression Algorithm

least_squares

Compute the coefficients of a polynomial expansion using least squares

orthogonal_matching_pursuit

Compute the coefficients of a polynomial expansion using orthogonal matching pursuit (OMP)

basis_pursuit

Compute the coefficients of a polynomial expansion by solving the Basis Pursuit \(\ell_1\) -minimization problem using linear programming.

basis_pursuit_denoising

Compute the coefficients of a polynomial expansion by solving the Basis Pursuit Denoising \(\ell_1\) -minimization problem using second order cone optimization.

least_angle_regression

Compute the coefficients of a polynomial expansion by using the greedy least angle regression (LAR) method.

least_absolute_shrinkage

Compute the coefficients of a polynomial expansion by using the LASSO problem.

Optional

cross_validation

Use cross validation to choose the ‘best’ polynomial order of a polynomial chaos expansion.

Optional

ratio_order

Specify a non-linear the relationship between the expansion order of a polynomial chaos expansion and the number of samples that will be used to compute the PCE coefficients.

Optional

response_scaling

Perform bounds-scaling on response values prior to surrogate emulation

Optional

use_derivatives

Use derivative data to construct surrogate models

Optional

tensor_grid

Use sub-sampled tensor-product quadrature points to build a polynomial chaos expansion.

Optional

reuse_points

This describes the behavior of reuse of points in constructing polynomial chaos expansion models.

Optional

max_solver_iterations

Maximum iterations in determining polynomial coefficients

Description

Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion. To avoid requiring the user to calculate N from n and p, the collocation_ratio allows for specification of a constant factor applied to N (e.g., collocation_ratio = 2. produces samples = 2N). In addition, the default linear relationship with N can be overridden using a real-valued exponent specified using ratio_order. In this case, the number of samples becomes \(cN^o\) where \(c\) is the collocation_ratio and \(o\) is the ratio_order. The use_derivatives flag informs the regression approach to include derivative matching equations (limited to gradients at present) in the least squares solutions, enabling the use of fewer collocation points for a given expansion order and dimension (number of points required becomes \(\frac{cN^o}{n+1}\) ).