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 
Automatic polynomial order refinement 

Optional 
Maximum number of expansion refinement iterations 

Optional 
Stopping criterion based on objective function or statistics convergence 

Optional 
define scaling of statistical metrics when adapting UQ surrogates 

Optional 
Type of solver for forming function train approximations by regression 

Optional 
Maximum iterations in determining polynomial coefficients 

Optional 
Maximum number of iterations for crossapproximation during a rank adaptation. 

Optional 
Convergence tolerance for the optimizer used during the regression solve. 

Optional 
Perform boundsscaling on response values prior to surrogate emulation 

Optional 
Use subsampled tensorproduct quadrature points to build a polynomial chaos expansion. 

Required (Choose One) 
Collocation Control 
Number of collocation points used to estimate expansion coefficients 

Set the number of points used to build a PCE via regression to be proportional to the number of terms in the expansion. 

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

Optional 
A secondary rounding tolerance used for postprocessing 

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

Optional 
Activate adaptive procedure for determining the best basis order 

Optional 
increment used when adapting the basis order in function train methods 

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

Optional 
Limit the number of crossvalidation candidates for basis order 

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

Optional 
Activate adaptive procedure for determining best rank representation 

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

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

Optional 
Limit the number of crossvalidation candidates for rank 

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

Optional 
Selection of sampling strategy 

Optional 
Selection of a random number generator 

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

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

Optional 
Values at which to estimate desired statistics for each response 

Optional 
Specify probability levels at which to estimate the corresponding response value 

Optional 
Specify reliability levels at which the response values will be estimated 

Optional 
Specify generalized relability levels at which to estimate the corresponding response value 

Optional 
Selection of cumulative or complementary cumulative functions 

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

Optional (Choose One) 
Covariance Type 
Display only the diagonal terms of the covariance matrix 

Display the full covariance matrix 

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

Optional 
Output file for surrogate model value evaluations 

Optional 
Seed of the random number generator 

Optional 
Reuses the same seed value for multiple random sampling sets 

Optional 
Identifier for model block to be used by a method 
Description
Tensor train decompositions are approximations that exploit low rank structure
in an inputoutput mapping. Refer to the function_train
surrogate model for additional details.
Usage Tips
This method is a selfcontained 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 = 1e12
rounding_tolerance = 1e12
convergence_tol = 1e6
collocation_points = 100
samples_on_emulator = 100000
seed = 531
response_levels = .1 1. 50. 100. 500. 1000.
variance_based_decomp