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