Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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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

Argument(s): REAL

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
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
(Choose One)
Group 1 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 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.

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 $\frac{cN^o}{n+1}$).