Streaming Total Dynamic Mode Decomposition (i.e. STDMD) is a variant of dynamic mode decomposition. More...

Inheritance diagram for STDMD:

Collaboration diagram for STDMD:

Public Member Functions
	TypeName ("STDMD")
	Runtime type information. More...

	STDMD (const fvMesh &mesh, const word &name, const dictionary &dict)
	Construct from components. More...

	STDMD (const STDMD &)=delete
	No copy construct. More...

void	operator= (const STDMD &)=delete
	No copy assignment. More...

virtual	~STDMD ()=default
	Destructor. More...

virtual bool	initialise (const RMatrix &z)
	Initialise 'Q' and 'G' (both require the first two snapshots) More...

virtual bool	update (const RMatrix &z)
	Incremental orthonormal basis update (K:Fig. 15) More...

virtual bool	fit ()

virtual bool	read (const dictionary &dict)
	Read STDMD settings. More...

Public Member Functions inherited from DMDModel
	TypeName ("DMDModel")
	Runtime type information. More...

	declareRunTimeSelectionTable (autoPtr, DMDModel, dictionary,(const fvMesh &mesh, const word &name, const dictionary &dict),(mesh, name, dict))

	DMDModel (const fvMesh &mesh, const word &name, const dictionary &dict)
	Construct from components. More...

	DMDModel (const DMDModel &)=delete
	No copy construct. More...

void	operator= (const DMDModel &)=delete
	No copy assignment. More...

virtual	~DMDModel ()=default
	Destructor. More...

virtual bool	initialise (const RMatrix &snapshot)=0
	Initialise model data members with a given snapshot. More...

virtual bool	update (const RMatrix &snapshot)=0
	Update model data members with a given snapshot. More...

virtual bool	fit ()=0

virtual void	reconstruct (const wordList modes)

virtual bool	read (const dictionary &dict)=0
	Read model settings. More...

Public Member Functions inherited from writeFile
	writeFile (const objectRegistry &obr, const fileName &prefix, const word &name="undefined", const bool writeToFile=true)
	Construct from objectRegistry, prefix, fileName. More...

	writeFile (const objectRegistry &obr, const fileName &prefix, const word &name, const dictionary &dict, const bool writeToFile=true)

	writeFile (const writeFile &wf)
	Construct copy. More...

virtual	~writeFile ()=default
	Destructor. More...

virtual bool	read (const dictionary &dict)
	Read. More...

virtual OFstream &	file ()
	Return access to the file (if only 1) More...

virtual bool	writeToFile () const
	Flag to allow writing to file. More...

virtual bool	canWriteHeader () const
	Flag to allow writing the header. More...

virtual label	charWidth () const
	Return width of character stream output. More...

virtual void	writeCommented (Ostream &os, const string &str) const
	Write a commented string to stream. More...

virtual void	writeTabbed (Ostream &os, const string &str) const
	Write a tabbed string to stream. More...

virtual void	writeHeader (Ostream &os, const string &str) const
	Write a commented header to stream. More...

virtual void	writeCurrentTime (Ostream &os) const
	Write the current time to stream. More...

virtual void	writeBreak (Ostream &os) const
	Write a break marker to the stream. More...

template<class Type >
void	writeHeaderValue (Ostream &os, const string &property, const Type &value) const
	Write a (commented) header property and value pair. More...

template<class Type >
void	writeValue (Ostream &os, const Type &val) const
	Write a given value to stream with the space delimiter. More...

Additional Inherited Members
Static Public Member Functions inherited from DMDModel
static autoPtr< DMDModel >	New (const fvMesh &mesh, const word &name, const dictionary &dict)
	Return a reference to the selected DMD model. More...

Static Public Attributes inherited from writeFile
static label	addChars = 8
	Additional characters for writing. More...

virtual bool	dynamics ()=0
	Compute and write mode dynamics. More...

virtual bool	modes ()=0
	Compute and write modes. More...

Protected Member Functions inherited from writeFile
void	initStream (Ostream &os) const
	Initialise the output stream for writing. More...

fileName	baseFileDir () const
	Return the base directory for output. More...

fileName	baseTimeDir () const
	Return the base directory for the current time value. More...

virtual autoPtr< OFstream >	createFile (const word &name, scalar timeValue) const
	Return autoPtr to a new file for a given time. More...

virtual autoPtr< OFstream >	createFile (const word &name) const
	Return autoPtr to a new file using the simulation start time. More...

virtual void	resetFile (const word &name)
	Reset internal file pointer to new file with new name. More...

Omanip< int >	valueWidth (const label offset=0) const
	Return the value width when writing to stream with optional offset. More...

void	operator= (const writeFile &)=delete
	No copy assignment. More...

Protected Attributes inherited from DMDModel
const fvMesh &	mesh_
	Reference to the mesh. More...

const word	name_
	Name of operand function object. More...

Protected Attributes inherited from writeFile
const objectRegistry &	fileObr_
	Reference to the region objectRegistry. More...

const fileName	prefix_
	Prefix. More...

word	fileName_
	Name of file. More...

autoPtr< OFstream >	filePtr_
	File pointer. More...

label	writePrecision_
	Write precision. More...

bool	writeToFile_
	Flag to enable/disable writing to file. More...

bool	updateHeader_

bool	writtenHeader_
	Flag to identify whether the header has been written. More...

bool	useUserTime_

scalar	startTime_
	Start time value. More...

Detailed Description

Streaming Total Dynamic Mode Decomposition (i.e. STDMD) is a variant of dynamic mode decomposition.

Among other Dynamic Mode Decomposition (DMD) variants, STDMD is presumed to provide the general DMD method capabilities alongside economised and feasible memory and CPU usage.

The code implementation corresponds to Figs. 15-16 of the first citation below, more broadly to Section 2.4.

References:

    DMD and mode-sorting algorithms (tags:K, HRDC, KZ, HWR):
        Kiewat, M. (2019).
        Streaming modal decomposition approaches for vehicle aerodynamics.
        PhD thesis. Munich: Technical University of Munich.
        URL:mediatum.ub.tum.de/doc/1482652/1482652.pdf

        Hemati, M. S., Rowley, C. W.,
        Deem, E. A., & Cattafesta, L. N. (2017).
        De-biasing the dynamic mode decomposition
        for applied Koopman spectral analysis of noisy datasets.
        Theoretical and Computational Fluid Dynamics, 31(4), 349-368.
        DOI:10.1007/s00162-017-0432-2

        Kou, J., & Zhang, W. (2017).
        An improved criterion to select
        dominant modes from dynamic mode decomposition.
        European Journal of Mechanics-B/Fluids, 62, 109-129.
        DOI:10.1016/j.euromechflu.2016.11.015

        Hemati, M. S., Williams, M. O., & Rowley, C. W. (2014).
        Dynamic mode decomposition for large and streaming datasets.
        Physics of Fluids, 26(11), 111701.
        DOI:10.1063/1.4901016

    Parallel classical Gram-Schmidt process (tag:Ka):
        Katagiri, T. (2003).
        Performance evaluation of parallel
        Gram-Schmidt re-orthogonalization methods.
        In: Palma J. M. L. M., Sousa A. A., Dongarra J., Hernández V. (eds)
        High Performance Computing for Computational Science — VECPAR 2002.
        Lecture Notes in Computer Science, vol 2565, p. 302-314.
        Berlin, Heidelberg: Springer.
        DOI:10.1007/3-540-36569-9_19

    Parallel direct tall-skinny QR decomposition (tags:BGD, DGHL):
        Benson, A. R., Gleich, D. F., & Demmel, J. (2013).
        Direct QR factorizations for
        tall-and-skinny matrices in MapReduce architectures.
        2013 IEEE International Conference on Big Data.
        DOI:10.1109/bigdata.2013.6691583

        Demmel, J., Grigori, L., Hoemmen, M., & Langou, J. (2012).
        Communication-optimal parallel
        and sequential QR and LU factorizations.
        SIAM Journal on Scientific Computing, 34(1), A206-A239.
        DOI:10.1137/080731992

Usage

Minimal example by using system/controlDict.functions:

DMD1
{
    // Mandatory entries
    DMDModel            STDMD;

    // Conditional mandatory entries

        // Option-1
        interval            5.5;

        // Option-2
        executeInterval     10;

    // Optional entries
    modeSorter          kiewat;
    nGramSchmidt        5;
    maxRank             50;
    nModes              50;
    fMin                0;
    fMax                1000000000;
    nAgglomerationProcs 20;

    // Optional entries (not recommended to change)
    minBasis            0.00000001;
    minEVal             0.00000001;
    sortLimiter         500.0;

    // Inherited entries
    ...
}

where the entries mean:

Property	Description	Type	Reqd	Deflt
`DMDModel`	Type: STDMD	word	yes	-
`interval`	STDMD time-step size [s]	scalar	cndtnl	executeInterval*(current time-step of the simulation)
`modeSorter`	Mode-sorting algorithm model	word	no	firstSnapshot
`nModes`	Number of output modes in input frequency range	label	no	GREAT
`maxRank`	Max columns in accumulated matrices	label	no	GREAT
`nGramSchmidt`	Number of Gram-Schmidt iterations	label	no	5
`fMin`	Min (non-negative) output frequency	label	no	0
`fMax`	Max output frequency	label	no	GREAT
`nAgglomerationProcs`	Number of processors at each agglomeration unit during the computation of reduced Koopman operator	label	no	20
`minBasis`	Orthogonal basis expansion threshold	scalar	no	1e-8
`minEVal`	Min eigenvalue for below eigenvalues are omitted	scalar	no	1e-8
`sortLimiter`	Max allowable magnitude for mag(eigenvalue)*(number of DMD steps) to be used in modeSorter={kiewat,kouZhang} to avoid overflow errors	scalar	no	500.0

Options for the modeSorter entry:

      kiewat        | Modified weighted-amplitude scaling method
      kouZhang      | Weighted-amplitude scaling method
      firstSnapshot | First-snapshot amplitude magnitude method

Note

To specify the STDMD time-step size (not necessarily equal to the time step of the simulation), entries of either interval or executeInterval must be available (highest to lowest precedence). While interval allows users to directly specify the STDMD time-step size in seconds, in absence of interval, for convenience, executeInterval allows users to compute the STDMD time-step internally by multiplying itself with the current time-step size of the simulation.
Limitation: Restart is currently not available since intermediate writing of STDMD matrices are not supported.
Limitation: Non-physical input (e.g. full-zero fields) can upset STDMD.
Warning: In modeSorter algorithms of kiewat and kouZhang, a function of \(power(x,y)\) exists where x is the magnitude of an eigenvalue, and y is the number of STDMD snapshots. This function poses a risk of overflow errors since, for example, if x ends up above 1.5 with 500 snapshots or more, this function automatically throws the floating point error meaning overflow. Therefore, the domain-range of this function is heuristically constrained by the optional entry sortLimiter which skips the evaluation of this function for a given mag(eigenvalue)*(no. of STDMD steps), i.e. x*y, whose magnitude is larger than sortLimiter.

See also

Source files

Definition at line 303 of file STDMD.H.

Constructor & Destructor Documentation

◆ STDMD() [1/2]

STDMD	(	const fvMesh &	mesh,
		const word &	name,
		const dictionary &	dict
	)

Construct from components.

Definition at line 808 of file STDMD.C.

◆ STDMD() [2/2]

STDMD ( const STDMD & )

delete

No copy construct.

◆ ~STDMD()

virtual ~STDMD ( )

virtualdefault

Destructor.

Member Function Documentation

◆ TypeName()

TypeName ( "STDMD" )

Runtime type information.

◆ operator=()

void operator= ( const STDMD & )

delete

No copy assignment.

◆ initialise()

bool initialise ( const RMatrix & z )

virtual

Initialise 'Q' and 'G' (both require the first two snapshots)

Implements DMDModel.

Definition at line 951 of file STDMD.C.

References UList< T >::begin(), Matrix< Form, Type >::cbegin(), Foam::fileHandler(), Matrix< Form, Type >::m(), Foam::mag(), IOobject::NO_READ, IOobject::NO_WRITE, Foam::sqr(), and fileOperation::writeObject().

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◆ update()

bool update ( const RMatrix & z )

virtual

Incremental orthonormal basis update (K:Fig. 15)

Working copy of the augmented snapshot matrix "z" being used in the classical Gram-Schmidt process

Implements DMDModel.

Definition at line 1012 of file STDMD.C.

◆ fit()

bool fit ( )

virtual

Compute and write modes and mode dynamics of model data members

Implements DMDModel.

Definition at line 1044 of file STDMD.C.

References splitCell::master(), and Foam::max().

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◆ read()

bool read ( const dictionary & dict )

virtual

Read STDMD settings.

Implements DMDModel.

Definition at line 864 of file STDMD.C.

References dict, e, Foam::endl(), MinMax< scalar >::ge(), MinMax< T >::ge(), Foam::Info, Foam::nl, and Foam::tab.

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The documentation for this class was generated from the following files:

src/functionObjects/field/DMD/DMDModels/derived/STDMD/STDMD.H
src/functionObjects/field/DMD/DMDModels/derived/STDMD/STDMD.C
src/functionObjects/field/DMD/DMDModels/derived/STDMD/STDMDTemplates.C

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ STDMD() [1/2]

◆ STDMD() [2/2]

◆ ~STDMD()

Member Function Documentation

◆ TypeName()

◆ operator=()

◆ initialise()

◆ update()

◆ fit()

◆ read()