1Blurb:: Multifidelity uncertainty quantification using function train expansions 2 3Description:: 4 5As described in the \ref method-function_train method and the 6\ref model-surrogate-global-function_train model, 7the function train (FT) approximation is a polynomial expansion that exploits low rank 8structure within the mapping from input random variables to output quantities of interest 9(QoI). For multilevel and multifidelity function train approximations, we decompose this 10expansion into several constituent expansions, one per model form or solution control 11level, where independent function train approximations are constructed for the 12low-fidelity/coarse resolution model and one or more levels of model discrepancy. 13 14In a three-model case with low-fidelity (L), medium-fidelity (M), and 15high-fidelity (H) models and an additive discrepancy approach, we can denote this as: 16 17\f[ Q^H \approx \hat{Q}_{r_L}^L + \hat{\Delta}_{r_{ML}}^{ML} + \hat{\Delta}_{r_{HM}}^{HM} \f] 18 19where \f$\Delta^{ij}\f$ represents a discrepancy expansion computed from 20\f$Q^i - Q^j\f$ and reduced rank representations of these discrepancies may 21be targeted (\f$ r_{HM} < r_{ML} < r_L \f$). 22 23In multifidelity approaches, sample allocation for the constituent expansions can be 24performed with either no, individual, or integrated adaptive refinement as described in 25\ref method-multifidelity_function_train-allocation_control. 26 27<b> Expected HDF5 Output </b> 28 29If Dakota was built with HDF5 support and run with the 30\ref environment-results_output-hdf5 keyword, this method 31writes the following results to HDF5: 32 33- \ref hdf5_results-se_moments (expansion moments only) 34- \ref hdf5_results-pdf 35- \ref hdf5_results-level_mappings 36 37In addition, the execution group has the attribute \c equiv_hf_evals, which 38records the equivalent number of high-fidelity evaluations. 39 40Topics:: 41 42Examples:: 43Theory:: 44Faq:: 45See_Also:: model-surrogate-global-function_train, method-function_train 46