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Dakota Reference Manual
Version 6.15
Explore and Predict with Confidence
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Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion.
Alias: none
Argument(s): REAL
Child Keywords:
Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description | |
---|---|---|---|---|
Optional (Choose One) | Regression Algorithm (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 ![]() | |||
basis_pursuit_denoising | Compute the coefficients of a polynomial expansion by solving the Basis Pursuit Denoising ![]() | |||
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 |
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 where
is the collocation_ratio and
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
).