Dakota Reference Manual
Version 6.12
Explore and Predict with Confidence

Multifidelity uncertainty quantification using function train expansions
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  allocation_control  Sample allocation approach for multifidelity expansions  
Optional  discrepancy_emulation  Formulation for emulation of model discrepancies.  
Optional  rounding_tolerance  An accuracy tolerance that is used to guide rounding during rank adaptation.  
Optional  arithmetic_tolerance  A secondary rounding tolerance used for postprocessing  
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 crossapproximation during a rank adaptation.  
Optional  solver_tolerance  Convergence tolerance for the optimizer used during the regression solve.  
Optional  tensor_grid  Use subsampled tensorproduct quadrature points to build a polynomial chaos expansion.  
Optional  collocation_points_sequence  Sequence of collocation point counts used in a multistage expansion  
Optional  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  start_order_sequence  Sequence of start orders used in a multistage expansion  
Optional  max_order  Maximum polynomial order of each univariate function within the functional tensor train.  
Optional  start_rank_sequence  Sequence of start ranks used in a multistage expansion  
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  adapt_rank  Activate adaptive procedure for determining best rank representation  
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 1)  diagonal_covariance  Display only the diagonal terms of the covariance matrix  
full_covariance  Display the full covariance matrix  
Optional  convergence_tolerance  Stopping criterion based on objective function or statistics convergence  
Optional  import_approx_points_file  Filename for points at which to evaluate the PCE/SC surrogate  
Optional  export_approx_points_file  Output file for evaluations of a surrogate model  
Optional  seed_sequence  Sequence of seed values for a multistage random sampling  
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 
As described in the function_train method and the function_train model, the function train (FT) approximation is a polynomial expansion that exploits low rank structure within the mapping from input random variables to output quantities of interest (QoI). For multilevel and multifidelity function train approximations, we decompose this expansion into several constituent expansions, one per model form or solution control level, where independent function train approximations are constructed for the lowfidelity/coarse resolution model and one or more levels of model discrepancy.
In a threemodel case with lowfidelity (L), mediumfidelity (M), and highfidelity (H) models and an additive discrepancy approach, we can denote this as:
where represents a discrepancy expansion computed from and reduced rank representations of these discrepancies may be targeted ( ).
In multifidelity approaches, sample allocation for the constituent expansions can be performed with either no, individual, or integrated adaptive refinement as described in allocation_control.
Expected HDF5 Output
If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5:
In addition, the execution group has the attribute equiv_hf_evals
, which records the equivalent number of highfidelity evaluations.
These keywords may also be of interest: