Dakota Reference Manual  Version 6.12
Explore and Predict with Confidence
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function_train


UQ method leveraging a functional tensor train surrogate model.

Specification

Alias: none

Argument(s): none

Child Keywords:

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Optional p_refinement Automatic polynomial order refinement
Optional max_refinement_iterations

Maximum number of expansion refinement iterations

Optional regression_type

Type of solver for forming function train approximations by regression

Optional max_solver_iterations

Maximum iterations in determining polynomial coefficients

Optional max_cross_iterations

Maximum number of iterations for cross-approximation during a rank adaptation.

Optional solver_tolerance

Convergence tolerance for the optimizer used during the regression solve.

Optional tensor_grid Use sub-sampled tensor-product quadrature points to build a polynomial chaos expansion.
Required
(Choose One)
Collocation Control (Group 1) collocation_points

Number of collocation points used to estimate expansion coefficients

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.

Optional rounding_tolerance

An accuracy tolerance that is used to guide rounding during rank adaptation.

Optional arithmetic_tolerance

A secondary rounding tolerance used for post-processing

Optional start_order

(Initial) polynomial order of each univariate function within the functional tensor train.

Optional max_order

Maximum polynomial order of each univariate function within the functional tensor train.

Optional start_rank

The initial rank used for the starting point during a rank adaptation.

Optional kick_rank

The increment in rank employed during each iteration of the rank adaptation.

Optional max_rank

Limits the maximum rank that is explored during a rank adaptation.

Optional adapt_rank

Activate adaptive procedure for determining best rank representation

Optional samples_on_emulator

Number of samples at which to evaluate an emulator (surrogate)

Optional sample_type

Selection of sampling strategy

Optional rng

Selection of a random number generator

Optional probability_refinement Allow refinement of probability and generalized reliability results using importance sampling
Optional final_moments

Output moments of the specified type and include them within the set of final statistics.

Optional response_levels

Values at which to estimate desired statistics for each response

Optional probability_levels Specify probability levels at which to estimate the corresponding response value
Optional reliability_levels Specify reliability levels at which the response values will be estimated
Optional gen_reliability_levels Specify generalized relability levels at which to estimate the corresponding response value
Optional distribution

Selection of cumulative or complementary cumulative functions

Optional variance_based_decomp

Activates global sensitivity analysis based on decomposition of response variance into main, interaction, and total effects

Optional
(Choose One)
Covariance Type (Group 2) diagonal_covariance Display only the diagonal terms of the covariance matrix
full_covariance Display the full covariance matrix
Optional convergence_tolerance

Stopping criterion based on objective function or statistics convergence

Optional import_approx_points_file

Filename for points at which to evaluate the PCE/SC surrogate

Optional export_approx_points_file

Output file for evaluations of a surrogate model

Optional seed

Seed of the random number generator

Optional fixed_seed

Reuses the same seed value for multiple random sampling sets

Optional model_pointer

Identifier for model block to be used by a method

Description

Tensor train decompositions are approximations that exploit low rank structure in an input-output mapping. Refer to the function_train surrogate model for additional details.

Usage Tips

This method is a self-contained method alternative to the function_train surrogate model specification, similar to current method specifications for polynomial chaos and stochastic collocation. In particular, this function_train method specification directly couples with a simulation model (optionally identified with a model_pointer) and an additional function train surrogate model specification is not required as these options have been embedded within the method specification.

Examples

method,
    function_train
      start_order = 2
      start_rank = 2  kick_rank = 2  max_rank = 10
      adapt_rank
      solver_tolerance    = 1e-12
      rounding_tolerance  = 1e-12
      convergence_tol     = 1e-6
      collocation_points  = 100
      samples_on_emulator = 100000
      seed = 531
      response_levels = .1 1. 50. 100. 500. 1000.
      variance_based_decomp

See Also

These keywords may also be of interest: