Nonintrusive polynomial chaos expansion approaches to uncertainty quantification. More...

Inheritance diagram for NonDPolynomialChaos:

Public Member Functions
	NonDPolynomialChaos (ProblemDescDB &problem_db, Model &model)
	standard constructor
	NonDPolynomialChaos (Model &model, short exp_coeffs_approach, const UShortArray &num_int_seq, const RealVector &dim_pref, short u_space_type, bool piecewise_basis, bool use_derivs)
	alternate constructor for numerical integration
	NonDPolynomialChaos (Model &model, short exp_coeffs_approach, const UShortArray &exp_order_seq, const RealVector &dim_pref, Real colloc_ratio, int seed, short u_space_type, bool piecewise_basis, bool use_derivs, bool cv_flag)
	alternate constructor for regression
	~NonDPolynomialChaos ()
	destructor
Protected Member Functions
void	derived_init_communicators (ParLevLIter pl_iter)
	derived class contributions to initializing the communicators associated with this Iterator instance
void	derived_set_communicators (ParLevLIter pl_iter)
	derived class contributions to setting the communicators associated with this Iterator instance
void	derived_free_communicators (ParLevLIter pl_iter)
	derived class contributions to freeing the communicators associated with this Iterator instance
void	resolve_inputs (short &u_space_type, short &data_order)
	perform error checks and mode overrides
void	initialize_u_space_model ()
	initialize uSpaceModel polynomial approximations with PCE/SC data
void	increment_specification_sequence ()
	increment the input specification sequence (PCE only)
void	compute_expansion ()
	form or import an orthogonal polynomial expansion using PCE methods
void	append (const RealMatrix &samples, const IntResponseMap &resp_map)
	append new data to uSpaceModel and update expansion order
void	increment_order_and_grid ()
	uniformly increment the order of the polynomial chaos expansion and define a consistent grid increment
void	print_coefficients (std::ostream &s)
	print the PCE coefficient array for the orthogonal basis
void	archive_coefficients ()
	archive the PCE coefficient array for the orthogonal basis
Private Member Functions
void	increment_grid_from_order ()
	define a grid increment that is consistent with an advancement in expansion order
void	increment_order_from_grid ()
	define an expansion order that is consistent with an advancement in structured/unstructured grid level/density
int	terms_ratio_to_samples (size_t num_exp_terms, Real colloc_ratio)
	convert number of expansion terms and collocation ratio to a number of collocation samples
Real	terms_samples_to_ratio (size_t num_exp_terms, int samples)
	convert number of expansion terms and number of collocation samples to a collocation ratio
void	ratio_samples_to_order (Real colloc_ratio, int num_samples, UShortArray &exp_order)
	convert collocation ratio and number of samples to expansion order
void	order_to_dim_preference (const UShortArray &order, unsigned short &p, RealVector &dim_pref)
	convert an isotropic/anisotropic expansion_order vector into a scalar plus a dimension preference vector
Private Attributes
String	expansionExportFile
	filename for export of chaos coefficients
String	expansionImportFile
	filename for import of chaos coefficients
Real	collocRatio
	factor applied to terms^termsOrder in computing number of regression points, either user specified or inferred
Real	termsOrder
	exponent applied to number of expansion terms for computing number of regression points
int	randomSeed
	seed for random number generator used for regression with LHS and sub-sampled tensor grids
bool	tensorRegression
	option for regression PCE using a filtered set tensor-product points
bool	crossValidation
	flag for use of cross-validation for selection of parameter settings in regression approaches
RealVector	noiseTols
	noise tolerance for compressive sensing algorithms; vector form used in cross-validation
Real	l2Penalty
	L2 penalty for LASSO algorithm (elastic net variant)
unsigned short	numAdvance
	number of frontier expansions per iteration with the ADAPTED_BASIS_EXPANDING_FRONT approach
UShortArray	expOrderSeqSpec
	user specification for expansion_order (array for multifidelity)
RealVector	dimPrefSpec
	user specification for dimension_preference
SizetArray	collocPtsSeqSpec
	user specification for collocation_points (array for multifidelity)
SizetArray	expSamplesSeqSpec
	user specification for expansion_samples (array for multifidelity)
size_t	sequenceIndex
	sequence index for {expOrder,collocPts,expSamples}SeqSpec
RealMatrix	pceGradsMeanX
	derivative of the PCE with respect to the x-space variables evaluated at the means (used as uncertainty importance metrics)
bool	normalizedCoeffOutput
	user request for use of normalization when outputting PCE coefficients

Detailed Description

Nonintrusive polynomial chaos expansion approaches to uncertainty quantification.

The NonDPolynomialChaos class uses a polynomial chaos expansion (PCE) approach to approximate the effect of parameter uncertainties on response functions of interest. It utilizes the OrthogPolyApproximation class to manage multiple types of orthogonal polynomials within a Wiener-Askey scheme to PCE. It supports PCE coefficient estimation via sampling, quadrature, point-collocation, and file import.

Constructor & Destructor Documentation

NonDPolynomialChaos	(	ProblemDescDB &	problem_db,
		Model &	model
	)

standard constructor

This constructor is called for a standard letter-envelope iterator instantiation using the ProblemDescDB.

References Dakota::abort_handler(), Response::active_set(), NonDIntegration::anisotropic_order_to_dimension_preference(), Model::assign_rep(), NonDPolynomialChaos::collocPtsSeqSpec, NonDPolynomialChaos::collocRatio, ParallelLibrary::command_line_check(), NonDExpansion::construct_cubature(), NonDExpansion::construct_expansion_sampler(), NonD::construct_lhs(), NonDExpansion::construct_quadrature(), NonDExpansion::construct_sparse_grid(), Model::current_response(), NonDIntegration::dimension_preference_to_anisotropic_order(), NonDPolynomialChaos::dimPrefSpec, NonDExpansion::expansionBasisType, NonDExpansion::expansionCoeffsApproach, NonDPolynomialChaos::expansionImportFile, NonDPolynomialChaos::expOrderSeqSpec, NonDPolynomialChaos::expSamplesSeqSpec, ProblemDescDB::get_bool(), ProblemDescDB::get_real(), ProblemDescDB::get_short(), ProblemDescDB::get_string(), ProblemDescDB::get_usa(), ProblemDescDB::get_ushort(), NonDExpansion::initialize(), NonDPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::maxEvalConcurrency, NonD::numContDesVars, NonD::numContEpistUncVars, Analyzer::numContinuousVars, NonD::numContStateVars, NonDExpansion::numSamplesOnModel, Iterator::outputLevel, Iterator::parallelLib, Iterator::probDescDB, NonDPolynomialChaos::randomSeed, NonDExpansion::refineControl, NonDExpansion::refineType, ActiveSet::request_values(), NonDPolynomialChaos::resolve_inputs(), NonDPolynomialChaos::sequenceIndex, NonDPolynomialChaos::tensorRegression, NonDPolynomialChaos::terms_ratio_to_samples(), NonDPolynomialChaos::terms_samples_to_ratio(), NonDPolynomialChaos::termsOrder, NonD::transform_model(), NonDExpansion::uSpaceModel, and Analyzer::vary_pattern().

NonDPolynomialChaos	(	Model &	model,
		short	exp_coeffs_approach,
		const UShortArray &	num_int_seq,
		const RealVector &	dim_pref,
		short	u_space_type,
		bool	piecewise_basis,
		bool	use_derivs
	)

alternate constructor for numerical integration

This constructor is used for helper iterator instantiation on the fly that employ numerical integration (quadrature, sparse grid, cubature).

References Response::active_set(), Model::assign_rep(), NonDExpansion::construct_cubature(), NonDExpansion::construct_quadrature(), NonDExpansion::construct_sparse_grid(), Model::current_response(), NonDExpansion::expansionCoeffsApproach, NonDExpansion::initialize(), NonDPolynomialChaos::initialize_u_space_model(), Iterator::iteratedModel, Iterator::outputLevel, ActiveSet::request_values(), NonDPolynomialChaos::resolve_inputs(), NonD::transform_model(), and NonDExpansion::uSpaceModel.

NonDPolynomialChaos	(	Model &	model,
		short	exp_coeffs_approach,
		const UShortArray &	exp_order_seq,
		const RealVector &	dim_pref,
		Real	colloc_ratio,
		int	seed,
		short	u_space_type,
		bool	piecewise_basis,
		bool	use_derivs,
		bool	cv_flag
	)