Dakota Reference Manual: function_train

| Dakota Reference Manual Version 6.15 Explore and Predict with Confidence

- Main Page
- Related Pages

All Pages
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 | convergence_tolerance | Stopping criterion based on objective function or statistics convergence
| Optional | metric_scale | define scaling of statistical metrics when adapting UQ surrogates
| 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 | response_scaling | Perform bounds-scaling on response values prior to surrogate emulation
| 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 | adapt_order | Activate adaptive procedure for determining the best basis order
| Optional | kick_order | increment used when adapting the basis order in function train methods
| Optional | max_order | Maximum polynomial order of each univariate function within the functional tensor train.
| Optional | max_cv_order_candidates | Limit the number of cross-validation candidates for basis order
| Optional | start_rank | The initial rank used for the starting point during a rank adaptation.
| Optional | adapt_rank | Activate adaptive procedure for determining best rank representation
| 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 | max_cv_rank_candidates | Limit the number of cross-validation candidates for rank
| 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 | import_approx_points_file | Filename for points at which to evaluate the PCE/SC surrogate
| Optional | export_approx_points_file | Output file for surrogate model value evaluations
| 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:

- function_train
- polynomial_chaos
- stoch_collocation