On the Effect of Quantization on Dynamic Mode Decomposition Article Swipe

PDF

Dilip Kumar Maity , Debdipta Goswami , Sriram Narayanan ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2404.02014

Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for estimating the Koopman Operator.This paper investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. This key theoretical finding paves the way to accurately recover the unquantized estimate from quantized data. We also explore the relationship between the two estimates in the finite data regime. The theory is validated through repeated numerical experiments conducted on three different dynamical systems.

Related Topics

Quantization (Signal Processing)

Human–Computer Interaction

Organic Chemistry

Concepts

Quantization (signal processing) Dynamic mode decomposition Mode (computer interface) Decomposition Mathematics Computer science Algorithm Chemistry Machine learning Human–computer interaction Organic chemistry

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2404.02014
PDF: https://arxiv.org/pdf/2404.02014
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4393941933

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4393941933

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2404.02014

Digital Object Identifier
Title: On the Effect of Quantization on Dynamic Mode Decomposition

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-04-02

Full publication date if available
Authors: Dilip Kumar Maity, Debdipta Goswami, Sriram Narayanan

List of authors in order
Landing page: https://arxiv.org/abs/2404.02014

Publisher landing page
PDF URL: https://arxiv.org/pdf/2404.02014

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2404.02014

Direct OA link when available
Concepts: Quantization (signal processing), Dynamic mode decomposition, Mode (computer interface), Decomposition, Mathematics, Computer science, Algorithm, Chemistry, Machine learning, Human–computer interaction, Organic chemistry

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4393941933
doi	https://doi.org/10.48550/arxiv.2404.02014
ids.doi	https://doi.org/10.48550/arxiv.2404.02014
ids.openalex	https://openalex.org/W4393941933
fwci
type	preprint
title	On the Effect of Quantization on Dynamic Mode Decomposition
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11324
topics[0].field.id	https://openalex.org/fields/13
topics[0].field.display_name	Biochemistry, Genetics and Molecular Biology
topics[0].score	0.8809999823570251
topics[0].domain.id	https://openalex.org/domains/1
topics[0].domain.display_name	Life Sciences
topics[0].subfield.id	https://openalex.org/subfields/1304
topics[0].subfield.display_name	Biophysics
topics[0].display_name	Spectroscopy Techniques in Biomedical and Chemical Research
topics[1].id	https://openalex.org/T10553
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.8320000171661377
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2206
topics[1].subfield.display_name	Computational Mechanics
topics[1].display_name	Combustion and flame dynamics
topics[2].id	https://openalex.org/T14257
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.8058000206947327
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2208
topics[2].subfield.display_name	Electrical and Electronic Engineering
topics[2].display_name	Advanced Measurement and Detection Methods
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C28855332
concepts[0].level	2
concepts[0].score	0.6927887201309204
concepts[0].wikidata	https://www.wikidata.org/wiki/Q198099
concepts[0].display_name	Quantization (signal processing)
concepts[1].id	https://openalex.org/C2777032711
concepts[1].level	2
concepts[1].score	0.6721152663230896
concepts[1].wikidata	https://www.wikidata.org/wiki/Q5318993
concepts[1].display_name	Dynamic mode decomposition
concepts[2].id	https://openalex.org/C48677424
concepts[2].level	2
concepts[2].score	0.47015810012817383
concepts[2].wikidata	https://www.wikidata.org/wiki/Q6888088
concepts[2].display_name	Mode (computer interface)
concepts[3].id	https://openalex.org/C124681953
concepts[3].level	2
concepts[3].score	0.4652830958366394
concepts[3].wikidata	https://www.wikidata.org/wiki/Q339062
concepts[3].display_name	Decomposition
concepts[4].id	https://openalex.org/C33923547
concepts[4].level	0
concepts[4].score	0.36341941356658936
concepts[4].wikidata	https://www.wikidata.org/wiki/Q395
concepts[4].display_name	Mathematics
concepts[5].id	https://openalex.org/C41008148
concepts[5].level	0
concepts[5].score	0.3321303725242615
concepts[5].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[5].display_name	Computer science
concepts[6].id	https://openalex.org/C11413529
concepts[6].level	1
concepts[6].score	0.22560113668441772
concepts[6].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[6].display_name	Algorithm
concepts[7].id	https://openalex.org/C185592680
concepts[7].level	0
concepts[7].score	0.09024971723556519
concepts[7].wikidata	https://www.wikidata.org/wiki/Q2329
concepts[7].display_name	Chemistry
concepts[8].id	https://openalex.org/C119857082
concepts[8].level	1
concepts[8].score	0.06364452838897705
concepts[8].wikidata	https://www.wikidata.org/wiki/Q2539
concepts[8].display_name	Machine learning
concepts[9].id	https://openalex.org/C107457646
concepts[9].level	1
concepts[9].score	0.05038243532180786
concepts[9].wikidata	https://www.wikidata.org/wiki/Q207434
concepts[9].display_name	Human–computer interaction
concepts[10].id	https://openalex.org/C178790620
concepts[10].level	1
concepts[10].score	0.0
concepts[10].wikidata	https://www.wikidata.org/wiki/Q11351
concepts[10].display_name	Organic chemistry
keywords[0].id	https://openalex.org/keywords/quantization
keywords[0].score	0.6927887201309204
keywords[0].display_name	Quantization (signal processing)
keywords[1].id	https://openalex.org/keywords/dynamic-mode-decomposition
keywords[1].score	0.6721152663230896
keywords[1].display_name	Dynamic mode decomposition
keywords[2].id	https://openalex.org/keywords/mode
keywords[2].score	0.47015810012817383
keywords[2].display_name	Mode (computer interface)
keywords[3].id	https://openalex.org/keywords/decomposition
keywords[3].score	0.4652830958366394
keywords[3].display_name	Decomposition
keywords[4].id	https://openalex.org/keywords/mathematics
keywords[4].score	0.36341941356658936
keywords[4].display_name	Mathematics
keywords[5].id	https://openalex.org/keywords/computer-science
keywords[5].score	0.3321303725242615
keywords[5].display_name	Computer science
keywords[6].id	https://openalex.org/keywords/algorithm
keywords[6].score	0.22560113668441772
keywords[6].display_name	Algorithm
keywords[7].id	https://openalex.org/keywords/chemistry
keywords[7].score	0.09024971723556519
keywords[7].display_name	Chemistry
keywords[8].id	https://openalex.org/keywords/machine-learning
keywords[8].score	0.06364452838897705
keywords[8].display_name	Machine learning
keywords[9].id	https://openalex.org/keywords/human–computer-interaction
keywords[9].score	0.05038243532180786
keywords[9].display_name	Human–computer interaction
language	en
locations[0].id	pmh:oai:arXiv.org:2404.02014
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license	cc-by-nc-sa
locations[0].pdf_url	https://arxiv.org/pdf/2404.02014
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id	https://openalex.org/licenses/cc-by-nc-sa
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2404.02014
locations[1].id	doi:10.48550/arxiv.2404.02014
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2404.02014
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5042246095
authorships[0].author.orcid	https://orcid.org/0000-0003-4284-3578
authorships[0].author.display_name	Dilip Kumar Maity
authorships[0].author_position	first
authorships[0].raw_author_name	Maity, Dipankar
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5044260875
authorships[1].author.orcid	https://orcid.org/0000-0002-5142-1222
authorships[1].author.display_name	Debdipta Goswami
authorships[1].author_position	middle
authorships[1].raw_author_name	Goswami, Debdipta
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5059216527
authorships[2].author.orcid	https://orcid.org/0000-0002-6484-2800
authorships[2].author.display_name	Sriram Narayanan
authorships[2].author_position	last
authorships[2].raw_author_name	Narayanan, Sriram
authorships[2].is_corresponding	False
has_content.pdf	True
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2404.02014
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	On the Effect of Quantization on Dynamic Mode Decomposition
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11324
primary_topic.field.id	https://openalex.org/fields/13
primary_topic.field.display_name	Biochemistry, Genetics and Molecular Biology
primary_topic.score	0.8809999823570251
primary_topic.domain.id	https://openalex.org/domains/1
primary_topic.domain.display_name	Life Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1304
primary_topic.subfield.display_name	Biophysics
primary_topic.display_name	Spectroscopy Techniques in Biomedical and Chemical Research
related_works	https://openalex.org/W2014356541, https://openalex.org/W2597763219, https://openalex.org/W2168222921, https://openalex.org/W1979597421, https://openalex.org/W2992578100, https://openalex.org/W2007980826, https://openalex.org/W3028908947, https://openalex.org/W2035021796, https://openalex.org/W2268351752, https://openalex.org/W2061531152
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2404.02014
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license	cc-by-nc-sa
best_oa_location.pdf_url	https://arxiv.org/pdf/2404.02014
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id	https://openalex.org/licenses/cc-by-nc-sa
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2404.02014
primary_location.id	pmh:oai:arXiv.org:2404.02014
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license	cc-by-nc-sa
primary_location.pdf_url	https://arxiv.org/pdf/2404.02014
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id	https://openalex.org/licenses/cc-by-nc-sa
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2404.02014
publication_date	2024-04-02
publication_year	2024
referenced_works_count	0
abstract_inverted_index.a	5, 59, 69
abstract_inverted_index.We	92
abstract_inverted_index.be	67
abstract_inverted_index.in	101
abstract_inverted_index.is	4, 21, 26, 108
abstract_inverted_index.of	36, 52, 72
abstract_inverted_index.on	115
abstract_inverted_index.to	83
abstract_inverted_index.we	29, 55
abstract_inverted_index.The	106
abstract_inverted_index.and	43
abstract_inverted_index.can	66
abstract_inverted_index.for	10
abstract_inverted_index.how	17
abstract_inverted_index.key	77
abstract_inverted_index.law	51
abstract_inverted_index.the	12, 18, 24, 31, 37, 50, 63, 73, 81, 86, 95, 98, 102
abstract_inverted_index.two	99
abstract_inverted_index.way	82
abstract_inverted_index.Mode	1
abstract_inverted_index.This	76
abstract_inverted_index.also	93
abstract_inverted_index.data	25, 42, 61, 104
abstract_inverted_index.from	40, 45, 89
abstract_inverted_index.used	7
abstract_inverted_index.when	23
abstract_inverted_index.(DMD)	3
abstract_inverted_index.data.	47, 91
abstract_inverted_index.large	53, 60
abstract_inverted_index.paper	15
abstract_inverted_index.paves	80
abstract_inverted_index.that,	57
abstract_inverted_index.those	44
abstract_inverted_index.three	116
abstract_inverted_index.under	58
abstract_inverted_index.using	49
abstract_inverted_index.finite	103
abstract_inverted_index.theory	107
abstract_inverted_index.widely	6
abstract_inverted_index.Dynamic	0
abstract_inverted_index.Koopman	13
abstract_inverted_index.between	34, 97
abstract_inverted_index.examine	30
abstract_inverted_index.explore	94
abstract_inverted_index.finding	79
abstract_inverted_index.process	20
abstract_inverted_index.recover	85
abstract_inverted_index.regime,	62
abstract_inverted_index.regime.	105
abstract_inverted_index.through	110
abstract_inverted_index.version	71
abstract_inverted_index.affected	22
abstract_inverted_index.estimate	65, 88
abstract_inverted_index.numbers,	54
abstract_inverted_index.obtained	39
abstract_inverted_index.operator	38
abstract_inverted_index.repeated	111
abstract_inverted_index.systems.	119
abstract_inverted_index.algorithm	9
abstract_inverted_index.conducted	114
abstract_inverted_index.different	117
abstract_inverted_index.dynamical	118
abstract_inverted_index.estimate.	75
abstract_inverted_index.estimates	35, 100
abstract_inverted_index.numerical	112
abstract_inverted_index.quantized	46, 64, 90
abstract_inverted_index.validated	109
abstract_inverted_index.accurately	84
abstract_inverted_index.connection	33
abstract_inverted_index.considered	68
abstract_inverted_index.estimating	11
abstract_inverted_index.estimation	19
abstract_inverted_index.quantized.	27
abstract_inverted_index.data-driven	8
abstract_inverted_index.demonstrate	56
abstract_inverted_index.experiments	113
abstract_inverted_index.fundamental	32
abstract_inverted_index.regularized	70
abstract_inverted_index.theoretical	78
abstract_inverted_index.unquantized	41, 74, 87
abstract_inverted_index.Furthermore,	48
abstract_inverted_index.investigates	16
abstract_inverted_index.relationship	96
abstract_inverted_index.Decomposition	2
abstract_inverted_index.Operator.This	14
abstract_inverted_index.Specifically,	28
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile