adamantine::DataAssimilator Class Reference

#include <DataAssimilator.hh>

Public Member Functions
	DataAssimilator (MPI_Comm const &global_communicator, MPI_Comm const &local_communicator, int my_color, boost::property_tree::ptree const &database)
void	update_ensemble (std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< double > const &expt_data, dealii::SparseMatrix< double > const &R)
template<int dim>
void	update_dof_mapping (std::pair< std::vector< int >, std::vector< int >> const &expt_to_dof_mapping)
template<int dim>
void	update_covariance_sparsity_pattern (dealii::DoFHandler< dim > const &dof_handler, const unsigned int parameter_size)

Private Types
using	block_size_type = dealii::LA::distributed::BlockVector< double >::size_type
using	TrilinosMatrixType = dealii::TrilinosWrappers::SparseMatrix
using	TrilinosSparsityPattern = dealii::TrilinosWrappers::SparsityPattern

Private Member Functions
void	gather_ensemble_members (std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> &global_augmented_state_ensemble, std::vector< unsigned int > &local_n_ensemble_members, std::vector< block_size_type > &block_sizes)
void	scatter_ensemble_members (std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> const &global_augmented_state_ensemble, std::vector< unsigned int > const &local_n_ensemble_members, std::vector< block_size_type > const &block_sizes)
std::vector< dealii::LA::distributed::BlockVector< double > >	apply_kalman_gain (std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, dealii::SparseMatrix< double > const &R, std::vector< dealii::Vector< double >> const &perturbed_innovation)
dealii::SparseMatrix< double >	calc_H (dealii::SparsityPattern &pattern) const
dealii::Vector< double >	calc_Hx (dealii::LA::distributed::Vector< double > const &sim_ensemble_member) const
void	fill_noise_vector (dealii::Vector< double > &vec, dealii::SparseMatrix< double > const &R, bool const R_is_diagonal)
double	gaspari_cohn_function (double const r) const
TrilinosMatrixType	calc_sample_covariance_sparse (std::vector< dealii::LA::distributed::BlockVector< double >> const &vec_ensemble) const

Private Attributes
MPI_Comm	_global_communicator
MPI_Comm	_local_communicator
int	_global_rank = -1
int	_global_comm_size = -1
int	_color = -1
unsigned int	_num_ensemble_members = 0
unsigned int	_sim_size = 0
unsigned int	_parameter_size = 0
unsigned int	_expt_size = 0
TrilinosSparsityPattern	_covariance_sparsity_pattern
std::map< const std::pair< unsigned int, unsigned int >, double >	_covariance_distance_map
double	_localization_cutoff_distance
LocalizationCutoff	_localization_cutoff_function
std::mt19937	_prng
std::normal_distribution	_normal_dist_generator
std::pair< std::vector< int >, std::vector< int > >	_expt_to_dof_mapping
dealii::SolverControl	_solver_control
dealii::SolverGMRES< dealii::Vector< double > >::AdditionalData	_additional_data

Friends
class	DataAssimilatorTester

Detailed Description

This class implements an ensemble Kalman filter (EnKF) for data assimilation. It updates an ensemble of solution vectors to be consistent with experimental observations.

The EnKF implementation here is largely based on Chapter 6 of Data Assimilation: Method and Applications by Asch, Bocquet, and Nodet.

Definition at line 62 of file DataAssimilator.hh.

Member Typedef Documentation

block_size_type

using adamantine::DataAssimilator::block_size_type = dealii::LA::distributed::BlockVector<double>::size_type

private

Definition at line 115 of file DataAssimilator.hh.

TrilinosMatrixType

using adamantine::DataAssimilator::TrilinosMatrixType = dealii::TrilinosWrappers::SparseMatrix

private

Definition at line 186 of file DataAssimilator.hh.

TrilinosSparsityPattern

using adamantine::DataAssimilator::TrilinosSparsityPattern = dealii::TrilinosWrappers::SparsityPattern

private

Definition at line 249 of file DataAssimilator.hh.

Constructor & Destructor Documentation

DataAssimilator()

adamantine::DataAssimilator::DataAssimilator	(	MPI_Comm const &	global_communicator,
		MPI_Comm const &	local_communicator,
		int	my_color,
		boost::property_tree::ptree const &	database
	)

Constructor.

Definition at line 36 of file DataAssimilator.cc.

Member Function Documentation

apply_kalman_gain()

std::vector< dealii::LA::distributed::BlockVector< double > > adamantine::DataAssimilator::apply_kalman_gain ( std::vector< dealii::LA::distributed::BlockVector< double >> &  augmented_state_ensemble, dealii::SparseMatrix< double > const &  R, std::vector< dealii::Vector< double >> const &  perturbed_innovation  )

private

This calculates the Kalman gain and applies it to the perturbed innovation.

Definition at line 404 of file DataAssimilator.cc.

calc_H()

dealii::SparseMatrix< double > adamantine::DataAssimilator::calc_H ( dealii::SparsityPattern &  pattern ) const

private

This calculates the observation matrix.

Definition at line 479 of file DataAssimilator.cc.

calc_Hx()

dealii::Vector< double > adamantine::DataAssimilator::calc_Hx ( dealii::LA::distributed::Vector< double > const &  sim_ensemble_member ) const

private

This calculates the application of the observation matrix on an unaugmented ensemble member from the simulation, avoiding explicit construction of a sparse matrix for H.

Definition at line 614 of file DataAssimilator.cc.

calc_sample_covariance_sparse()

DataAssimilator::TrilinosMatrixType adamantine::DataAssimilator::calc_sample_covariance_sparse ( std::vector< dealii::LA::distributed::BlockVector< double >> const &  vec_ensemble ) const

private

This calculates the sample covariance for an input ensemble of vectors (vec_ensemble). Currently this is tied to the simulation ensemble, through the use of member variables inside. If needed, the interface could be redone to make it more generally applicable.

Definition at line 691 of file DataAssimilator.cc.

fill_noise_vector()

void adamantine::DataAssimilator::fill_noise_vector ( dealii::Vector< double > &  vec, dealii::SparseMatrix< double > const &  R, bool const  R_is_diagonal  )

private

This fills a vector (vec) with noise from a multivariate normal distribution defined by a covariance matrix (R). Note: For non-diagonal R this method currently uses full matrices, which substantially limits the allowable problem size.

Definition at line 630 of file DataAssimilator.cc.

gaspari_cohn_function()

double adamantine::DataAssimilator::gaspari_cohn_function ( double const  r ) const

private

A standard localization function, resembles a Gaussian, but with finite support. From Gaspari and Cohn, Quarterly Journal of the Royal Meteorological Society, 125, 1999.

Definition at line 672 of file DataAssimilator.cc.

gather_ensemble_members()

void adamantine::DataAssimilator::gather_ensemble_members ( std::vector< dealii::LA::distributed::BlockVector< double >> &  augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> &  global_augmented_state_ensemble, std::vector< unsigned int > &  local_n_ensemble_members, std::vector< block_size_type > &  block_sizes  )

private

Gather the augmented ensemble members on the global root node in order to apply the Kalman gain.

Definition at line 191 of file DataAssimilator.cc.

scatter_ensemble_members()

void adamantine::DataAssimilator::scatter_ensemble_members ( std::vector< dealii::LA::distributed::BlockVector< double >> &  augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> const &  global_augmented_state_ensemble, std::vector< unsigned int > const &  local_n_ensemble_members, std::vector< block_size_type > const &  block_sizes  )

private

Scatter the global_augmented_state_ensemble back into augmented_state_ensemble.

Definition at line 305 of file DataAssimilator.cc.

update_covariance_sparsity_pattern()

template<int dim>

template void adamantine::DataAssimilator::update_covariance_sparsity_pattern< 3 >	(	dealii::DoFHandler< dim > const &	dof_handler,
		const unsigned int	parameter_size
	)

This updates the sparsity pattern for the sample covariance matrix for the simulation ensemble. This must be called before updateEnsemble whenever there are changes to the simulation mesh.

Definition at line 513 of file DataAssimilator.cc.

update_dof_mapping()

template<int dim>

template void adamantine::DataAssimilator::update_dof_mapping< 3 >

(

std::pair< std::vector< int >, std::vector< int >> const &

expt_to_dof_mapping

)

This updates the internal mapping between the indices of the entries in expt_data and the indices of the entries in the sim_data ensemble members in updateEnsemble. This must be called before updateEnsemble whenever there are changes to the simulation mesh or the observation locations.

Definition at line 505 of file DataAssimilator.cc.

update_ensemble()

void adamantine::DataAssimilator::update_ensemble	(	std::vector< dealii::LA::distributed::BlockVector< double >> &	augmented_state_ensemble,
		std::vector< double > const &	expt_data,
		dealii::SparseMatrix< double > const &	R
	)

This is the main public interface for the class and is called to perform one assimilation process. It takes in an ensemble of simulation data (sim_data), experimental observation data (expt_data), and the covariance matrix for the experimental observations (R). This function updates sim_data using the EnKF method.

Overall it performs x = x + K (y + u - H x) for each ensemble member, where: x is the simulation solution K is the Kalman gain y is the observed solution u is a perturbation to the observed solution H is the observation matrix

Definition at line 95 of file DataAssimilator.cc.

Friends And Related Function Documentation

DataAssimilatorTester

friend class DataAssimilatorTester

friend

Definition at line 64 of file DataAssimilator.hh.

Member Data Documentation

_additional_data

dealii::SolverGMRES<dealii::Vector<double> >::AdditionalData adamantine::DataAssimilator::_additional_data

private

Additional settings for the GMRES solver needed for the matrix inversion in the Kalman gain calculation.

Definition at line 307 of file DataAssimilator.hh.

_color

int adamantine::DataAssimilator::_color = -1

private

Color associated with the local

Definition at line 222 of file DataAssimilator.hh.

_covariance_distance_map

std::map<const std::pair<unsigned int, unsigned int>, double> adamantine::DataAssimilator::_covariance_distance_map

private

Map between the indices in the covariance matrix and the distance between the support points for the associated dofs on the mesh. This is necessary for localization.

Definition at line 263 of file DataAssimilator.hh.

_covariance_sparsity_pattern

TrilinosSparsityPattern adamantine::DataAssimilator::_covariance_sparsity_pattern

private

The sparsity pattern for the localized covariance matrix.

Definition at line 255 of file DataAssimilator.hh.

_expt_size

unsigned int adamantine::DataAssimilator::_expt_size = 0

private

The length of the data vector the experimental observations.

Definition at line 242 of file DataAssimilator.hh.

_expt_to_dof_mapping

std::pair<std::vector<int>, std::vector<int> > adamantine::DataAssimilator::_expt_to_dof_mapping

private

The mapping between the index in the experimental observation data vector to the DoF in the simulation data vectors. This is simpler to use than the indices and offsets that are passed into updateEnsemble, and means that the simulation DoFHandler only needs to be used by updateDofMapping where this variable is set.

Definition at line 295 of file DataAssimilator.hh.

_global_comm_size

int adamantine::DataAssimilator::_global_comm_size = -1

private

Number of processes in the gglbal MPI communicator.

Definition at line 217 of file DataAssimilator.hh.

_global_communicator

MPI_Comm adamantine::DataAssimilator::_global_communicator

private

Global MPI communicator.

Definition at line 202 of file DataAssimilator.hh.

_global_rank

int adamantine::DataAssimilator::_global_rank = -1

private

Rank of the process when using the global MPI communicator.

Definition at line 212 of file DataAssimilator.hh.

_local_communicator

MPI_Comm adamantine::DataAssimilator::_local_communicator

private

Local MPI communicator split off the global MPI communicator.

Definition at line 207 of file DataAssimilator.hh.

_localization_cutoff_distance

double adamantine::DataAssimilator::_localization_cutoff_distance

private

The distance at which the sample covariance is truncated.

Definition at line 268 of file DataAssimilator.hh.

_localization_cutoff_function

LocalizationCutoff adamantine::DataAssimilator::_localization_cutoff_function

private

The function used to reduce the sample covariance entries based on the distance between the relevant points.

Definition at line 274 of file DataAssimilator.hh.

_normal_dist_generator

std::normal_distribution adamantine::DataAssimilator::_normal_dist_generator

private

Random variate generator for a normal distribution, used for the perturbations to the innovation vectors.

Definition at line 286 of file DataAssimilator.hh.

_num_ensemble_members

unsigned int adamantine::DataAssimilator::_num_ensemble_members = 0

private

The number of ensemble members in the simulation.

Definition at line 227 of file DataAssimilator.hh.

_parameter_size

unsigned int adamantine::DataAssimilator::_parameter_size = 0

private

The length of the parameter vector for each simulation ensemble member.

Definition at line 237 of file DataAssimilator.hh.

_prng

std::mt19937 adamantine::DataAssimilator::_prng

private

The pseudo-random number generator, used for the perturbations to the innovation vectors.

Definition at line 280 of file DataAssimilator.hh.

_sim_size

unsigned int adamantine::DataAssimilator::_sim_size = 0

private

The length of the data vector for each simulation ensemble member.

Definition at line 232 of file DataAssimilator.hh.

_solver_control

dealii::SolverControl adamantine::DataAssimilator::_solver_control

private

Standardized settings for the GMRES solver needed for the matrix inversion in the Kalman gain calculation.

Definition at line 301 of file DataAssimilator.hh.