ModelEvaluator for forming adjoint sensitivity equations. More...

#include <Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp>

Inheritance diagram for Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >:

Public Types
typedef Thyra::VectorBase< Scalar >	Vector
typedef Thyra::MultiVectorBase< Scalar >	MultiVector

Public Member Functions
	AdjointAuxSensitivityModelEvaluator (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &model, const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &adjoint_model, const Scalar &t_init, const Scalar &t_final, const Teuchos::RCP< const Teuchos::ParameterList > &pList=Teuchos::null)
	Constructor.
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getModel () const
	Get the underlying model 'f'.
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getAdjointModel () const
	Get the underlying adjoint model.
void	setFinalTime (const Scalar t_final)
	Set the final time from the forward evaluation.
void	setForwardSolutionHistory (const Teuchos::RCP< const Tempus::SolutionHistory< Scalar > > &sh)
	Set solution history from forward evaluation.

Public functions overridden from ModelEvaulator.
typedef Thyra::DefaultProductVectorSpace< Scalar >	DPVS
typedef Thyra::DefaultProductVector< Scalar >	DPV
typedef Thyra::DefaultMultiVectorProductVectorSpace< Scalar >	DMVPVS
typedef Thyra::DefaultMultiVectorProductVector< Scalar >	DMVPV
Thyra::ModelEvaluatorBase::InArgs< Scalar >	prototypeInArgs_
Thyra::ModelEvaluatorBase::OutArgs< Scalar >	prototypeOutArgs_
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	model_
Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	adjoint_model_
Teuchos::RCP< const DMVPVS >	adjoint_space_
Teuchos::RCP< const DMVPVS >	residual_space_
Teuchos::RCP< const DMVPVS >	response_space_
Teuchos::RCP< const DPVS >	x_prod_space_
Teuchos::RCP< const DPVS >	f_prod_space_
Teuchos::RCP< const Tempus::SolutionHistory< Scalar > >	sh_
Scalar	t_init_
Scalar	t_final_
bool	mass_matrix_is_constant_
bool	mass_matrix_is_identity_
AdjointResponseType	response_type_
bool	g_depends_on_p_
bool	f_depends_on_p_
int	p_index_
int	g_index_
int	num_adjoint_
bool	mass_matrix_is_computed_
Teuchos::RCP< Thyra::LinearOpBase< Scalar > >	my_dfdx_
Teuchos::RCP< Thyra::LinearOpBase< Scalar > >	my_dfdxdot_
Teuchos::RCP< Thyra::LinearOpBase< Scalar > >	my_dfdp_op_
Teuchos::RCP< Thyra::MultiVectorBase< Scalar > >	my_dfdp_mv_
Teuchos::RCP< Thyra::MultiVectorBase< Scalar > >	my_dgdx_mv_
Teuchos::RCP< Thyra::MultiVectorBase< Scalar > >	my_dgdp_mv_
bool	dgdx_dot_checked_
Teuchos::RCP< Tempus::SolutionState< Scalar > >	forward_state_
Scalar	t_interp_
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_p_space (int p) const
Teuchos::RCP< const Teuchos::Array< std::string > >	get_p_names (int p) const
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_x_space () const
Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > >	get_f_space () const
Teuchos::RCP< Thyra::LinearOpBase< Scalar > >	create_W_op () const
Teuchos::RCP< const Thyra::LinearOpWithSolveFactoryBase< Scalar > >	get_W_factory () const
Thyra::ModelEvaluatorBase::InArgs< Scalar >	createInArgs () const
Thyra::ModelEvaluatorBase::InArgs< Scalar >	getNominalValues () const
static Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters ()
Thyra::ModelEvaluatorBase::OutArgs< Scalar >	createOutArgsImpl () const
void	evalModelImpl (const Thyra::ModelEvaluatorBase::InArgs< Scalar > &inArgs, const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &outArgs) const
Thyra::ModelEvaluatorBase::InArgs< Scalar >	responseInArgs (const Thyra::ModelEvaluatorBase::InArgs< Scalar > &me_inArgs) const
	InArgs for evaluating the response derivatives at the forward state.

Detailed Description

template<typename Scalar>
class Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >

ModelEvaluator for forming adjoint sensitivity equations.

This class wraps a given ModelEvalutor encapsulating f(x_dot,x,p) and creates a new "residual" for the adjoint sensitivity equations: F(y,z) = [ d/dt( df/dx_dot^T*y ) - df/dx^T*y ] = 0 [ dz/dt - df/dp^T*y ] where y is the adjoint variable and z is an auxiliary variable. Nominally y is a multi-vector belonging to the vector space of the residual f and a given number of columns and z is a multi-vector beling to the vector space p and the same number of columns. To satisfy the model evaluator interface, y and z are converted to a product vector formed by their columns. This is the form of the adjoint equations suitable for computing sensitivities of a response function g(x(T),p).

To compute adjoint sensitivities, the equations f(x_dot,x,p) = 0 are integrated forward in time to some final time T, with the adjoint equations above integrated backward in time starting at T. Since the tempus integrator can only integrate forward in time, we define tau = T - t and transform the adjoint equations to: F(y) = d/dtau( df/dx_dot^T*y ) + df/dx^T*y = 0. The initial conditions at t = T for y are y(T) = df/dx_dot(x_dot(T),x(T),p)^{-T} * dg/dx(x(T),p)^T. along with z(T) = 0. The sensitivity of g(T) is then dg/dp(T) - int_{0}^T(df/dp^T*y)dt + dx/dp(0)^T*df/dx_dot(0)^T*y(0) = dg/dp(T) - z(0) + dx/dp(0)^T*df/dx_dot(0)^T*y(0)

This model evaluator supports both implicit and explict forms of the governing equations. However it assumes df/dx_dot is constant with respect to x_dot, x, and t so that the adjoint equations become F(y) = df/dxdot^T*y_dot + df/dx^T*y = 0. Moving beyond this assumption will require modifications to the steppers in how they generate time-derivative terms.

For a time-integrated response J = int_{0}^T g(x(t),p,t) dt ("Response Type" = "Time Integral"), the response enters the adjoint equations as a source term. In the reversed time tau the equations become F(y,z) = [ df/dx_dot^T*y_dot + df/dx^T*y - dg/dx^T ] = 0 [ dz/dtau - df/dp^T*y + dg/dp^T ] (explicit form: y_dot = -df/dx^T*y + dg/dx^T, z_dot = df/dp^T*y - dg/dp^T), with y = 0 and z = 0 at t = T, and the sensitivity of J is -z(0) + dx/dp(0)^T*df/dx_dot(0)^T*y(0). The response must not depend on x_dot. For "Final Time" and "Sum Over Times" responses the adjoint equations are homogeneous; the response terms are added by IntegratorAdjointSensitivity.

Definition at line 71 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

Member Typedef Documentation

◆ Vector

template<typename Scalar>

typedef Thyra::VectorBase<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::Vector

Definition at line 74 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ MultiVector

template<typename Scalar>

typedef Thyra::MultiVectorBase<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::MultiVector

Definition at line 75 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ DPVS

template<typename Scalar>

typedef Thyra::DefaultProductVectorSpace<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::DPVS

private

Definition at line 158 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ DPV

template<typename Scalar>

typedef Thyra::DefaultProductVector<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::DPV

private

Definition at line 159 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ DMVPVS

template<typename Scalar>

typedef Thyra::DefaultMultiVectorProductVectorSpace<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::DMVPVS

private

Definition at line 160 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ DMVPV

template<typename Scalar>

typedef Thyra::DefaultMultiVectorProductVector<Scalar> Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::DMVPV

private

Definition at line 161 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

Constructor & Destructor Documentation

◆ AdjointAuxSensitivityModelEvaluator()

template<typename Scalar>

Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::AdjointAuxSensitivityModelEvaluator	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	model,
		const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	adjoint_model,
		const Scalar &	t_init,
		const Scalar &	t_final,
		const Teuchos::RCP< const Teuchos::ParameterList > &	pList = Teuchos::null )

Constructor.

t_final is the final integration time used to implement the time transformation described above. num_adjoint is the number of adjoint variables defining the number of columns in y, which is determined by the number of elements in the vector space for the response g. The optionally supplied parameter list supports the following options:

"Sensitivity Parameter Index", (default: 0) The model evaluator parameter index for which sensitivities will be computed.
"Response Function Index", (default: 0) The model evaluator response index for which sensitivities will be computed.
"Mass Matrix Is Constant" (default: true) Whether the mass matrix df/dx_dot is a constant matrix. As describe above, this is currently required to be true.
"Mass Matrix Is Identity" (default: false) Whether the mass matrix is the identity matrix, in which some computations can be skipped.
"Response Type" (default: "Final Time") "Final Time", "Time Integral" or "Sum Over Times" (see IntegratorAdjointSensitivity). Only "Time Integral" changes the adjoint equations.
"Response Time List" (default: "") Times of the "Sum Over Times" response (not used by this model evaluator).
"Response Depends on Parameters" (default: true) Whether the response depends on the parameters. If false, dg/dp is not evaluated for a "Time Integral" response.
"Residual Depends on Parameters" (default: true) Whether the residual depends on the parameters. If false, df/dp is not evaluated and the auxiliary integral does not include it.

Definition at line 25 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

Member Function Documentation

◆ getModel()

template<typename Scalar>

Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::getModel ( ) const

inline

Get the underlying model 'f'.

Definition at line 115 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ getAdjointModel()

template<typename Scalar>

Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::getAdjointModel ( ) const

inline

Get the underlying adjoint model.

Definition at line 121 of file Tempus_AdjointAuxSensitivityModelEvaluator_decl.hpp.

◆ setFinalTime()

template<typename Scalar>

void Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::setFinalTime ( const Scalar t_final )

Set the final time from the forward evaluation.

Definition at line 117 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ setForwardSolutionHistory()

template<typename Scalar>

void Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::setForwardSolutionHistory ( const Teuchos::RCP< const Tempus::SolutionHistory< Scalar > > & sh )

Set solution history from forward evaluation.

Definition at line 124 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ get_p_space()

template<typename Scalar>

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::get_p_space ( int p ) const

Definition at line 135 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ get_p_names()

template<typename Scalar>

Teuchos::RCP< const Teuchos::Array< std::string > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::get_p_names ( int p ) const

Definition at line 143 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ get_x_space()

template<typename Scalar>

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::get_x_space ( ) const

Definition at line 151 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ get_f_space()

template<typename Scalar>

Teuchos::RCP< const Thyra::VectorSpaceBase< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::get_f_space ( ) const

Definition at line 158 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ create_W_op()

template<typename Scalar>

Teuchos::RCP< Thyra::LinearOpBase< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::create_W_op ( ) const

Definition at line 165 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ get_W_factory()

template<typename Scalar>

Teuchos::RCP< const Thyra::LinearOpWithSolveFactoryBase< Scalar > > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::get_W_factory ( ) const

Definition at line 181 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ createInArgs()

template<typename Scalar>

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::createInArgs ( ) const

Definition at line 206 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ getNominalValues()

template<typename Scalar>

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::getNominalValues ( ) const

Definition at line 213 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ getValidParameters()

template<class Scalar>

Teuchos::RCP< const Teuchos::ParameterList > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::getValidParameters ( )

static

Definition at line 427 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ createOutArgsImpl()

template<typename Scalar>

Thyra::ModelEvaluatorBase::OutArgs< Scalar > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::createOutArgsImpl ( ) const

private

Definition at line 243 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ evalModelImpl()

template<typename Scalar>

void Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::evalModelImpl	(	const Thyra::ModelEvaluatorBase::InArgs< Scalar > &	inArgs,
		const Thyra::ModelEvaluatorBase::OutArgs< Scalar > &	outArgs ) const

private

Definition at line 249 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.

◆ responseInArgs()

template<typename Scalar>

Thyra::ModelEvaluatorBase::InArgs< Scalar > Tempus::AdjointAuxSensitivityModelEvaluator< Scalar >::responseInArgs ( const Thyra::ModelEvaluatorBase::InArgs< Scalar > & me_inArgs ) const

private

InArgs for evaluating the response derivatives at the forward state.

Definition at line 448 of file Tempus_AdjointAuxSensitivityModelEvaluator_impl.hpp.