.. _method-function_train: """""""""""""" function_train """""""""""""" UQ method leveraging a functional tensor train surrogate model. .. toctree:: :hidden: :maxdepth: 1 method-function_train-p_refinement method-function_train-max_refinement_iterations method-function_train-convergence_tolerance method-function_train-metric_scale method-function_train-regression_type method-function_train-max_solver_iterations method-function_train-max_cross_iterations method-function_train-solver_tolerance method-function_train-response_scaling method-function_train-tensor_grid method-function_train-collocation_points method-function_train-collocation_ratio method-function_train-rounding_tolerance method-function_train-arithmetic_tolerance method-function_train-start_order method-function_train-adapt_order method-function_train-kick_order method-function_train-max_order method-function_train-max_cv_order_candidates method-function_train-start_rank method-function_train-adapt_rank method-function_train-kick_rank method-function_train-max_rank method-function_train-max_cv_rank_candidates method-function_train-samples_on_emulator method-function_train-sample_type method-function_train-rng method-function_train-probability_refinement method-function_train-final_moments method-function_train-response_levels method-function_train-probability_levels method-function_train-reliability_levels method-function_train-gen_reliability_levels method-function_train-distribution method-function_train-variance_based_decomp method-function_train-diagonal_covariance method-function_train-full_covariance method-function_train-import_approx_points_file method-function_train-export_approx_points_file method-function_train-seed method-function_train-fixed_seed method-function_train-model_pointer **Specification** - *Alias:* None - *Arguments:* None **Child Keywords:** +-------------------------+--------------------+-------------------------------+---------------------------------------------+ | Required/Optional | Description of | Dakota Keyword | Dakota Keyword Description | | | Group | | | +=========================+====================+===============================+=============================================+ | 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 | `collocation_points`__ | Number of collocation points used to | | | Control | | 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 | +----------------------------------------------+-------------------------------+---------------------------------------------+ .. __: method-function_train-p_refinement.html __ method-function_train-max_refinement_iterations.html __ method-function_train-convergence_tolerance.html __ method-function_train-metric_scale.html __ method-function_train-regression_type.html __ method-function_train-max_solver_iterations.html __ method-function_train-max_cross_iterations.html __ method-function_train-solver_tolerance.html __ method-function_train-response_scaling.html __ method-function_train-tensor_grid.html __ method-function_train-collocation_points.html __ method-function_train-collocation_ratio.html __ method-function_train-rounding_tolerance.html __ method-function_train-arithmetic_tolerance.html __ method-function_train-start_order.html __ method-function_train-adapt_order.html __ method-function_train-kick_order.html __ method-function_train-max_order.html __ method-function_train-max_cv_order_candidates.html __ method-function_train-start_rank.html __ method-function_train-adapt_rank.html __ method-function_train-kick_rank.html __ method-function_train-max_rank.html __ method-function_train-max_cv_rank_candidates.html __ method-function_train-samples_on_emulator.html __ method-function_train-sample_type.html __ method-function_train-rng.html __ method-function_train-probability_refinement.html __ method-function_train-final_moments.html __ method-function_train-response_levels.html __ method-function_train-probability_levels.html __ method-function_train-reliability_levels.html __ method-function_train-gen_reliability_levels.html __ method-function_train-distribution.html __ method-function_train-variance_based_decomp.html __ method-function_train-diagonal_covariance.html __ method-function_train-full_covariance.html __ method-function_train-import_approx_points_file.html __ method-function_train-export_approx_points_file.html __ method-function_train-seed.html __ method-function_train-fixed_seed.html __ method-function_train-model_pointer.html **Description** Tensor train decompositions are approximations that exploit low rank structure in an input-output mapping. Refer to the :dakkw:`model-surrogate-global-function_train` surrogate model for additional details. *Usage Tips* This method is a self-contained method alternative to the :dakkw:`model-surrogate-global-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** .. code-block:: 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