function_train

UQ method leveraging a functional tensor train surrogate model.

Specification

  • Alias: None

  • Arguments: 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

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

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