Deep Koopman learning of nonlinear time-varying systems Article Swipe

View

Wenjian Hao , Bowen Huang , Wei Pan , Di Wu , Shaoshuai Mou ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1016/j.automatica.2023.111372

Related Topics

Artificial Intelligence

Concepts

Nonlinear system Artificial neural network Control theory (sociology) Computer science Deep learning Operator (biology) Approximation error Linear approximation Nonlinear dynamical systems Applied mathematics Mathematics Algorithm Artificial intelligence Physics Control (management) Chemistry Repressor Transcription factor Gene Quantum mechanics Biochemistry

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.1016/j.automatica.2023.111372
OA Status: green
Cited By: 13
References: 27
Related Works: 10
OpenAlex ID: https://openalex.org/W4387853540

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4387853540

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.1016/j.automatica.2023.111372

Digital Object Identifier
Title: Deep Koopman learning of nonlinear time-varying systems

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-10-21

Full publication date if available
Authors: Wenjian Hao, Bowen Huang, Wei Pan, Di Wu, Shaoshuai Mou

List of authors in order
Landing page: https://doi.org/10.1016/j.automatica.2023.111372

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://www.osti.gov/biblio/2293484

Direct OA link when available
Concepts: Nonlinear system, Artificial neural network, Control theory (sociology), Computer science, Deep learning, Operator (biology), Approximation error, Linear approximation, Nonlinear dynamical systems, Applied mathematics, Mathematics, Algorithm, Artificial intelligence, Physics, Control (management), Chemistry, Repressor, Transcription factor, Gene, Quantum mechanics, Biochemistry

Top concepts (fields/topics) attached by OpenAlex
Cited by: 13

Total citation count in OpenAlex
Citations by year (recent): 2025: 11, 2024: 2

Per-year citation counts (last 5 years)
References (count): 27

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4387853540
doi	https://doi.org/10.1016/j.automatica.2023.111372
ids.doi	https://doi.org/10.1016/j.automatica.2023.111372
ids.openalex	https://openalex.org/W4387853540
fwci	2.80377728
type	article
title	Deep Koopman learning of nonlinear time-varying systems
biblio.issue
biblio.volume	159
biblio.last_page	111372
biblio.first_page	111372
topics[0].id	https://openalex.org/T11206
topics[0].field.id	https://openalex.org/fields/31
topics[0].field.display_name	Physics and Astronomy
topics[0].score	1.0
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/3109
topics[0].subfield.display_name	Statistical and Nonlinear Physics
topics[0].display_name	Model Reduction and Neural Networks
topics[1].id	https://openalex.org/T10928
topics[1].field.id	https://openalex.org/fields/18
topics[1].field.display_name	Decision Sciences
topics[1].score	0.9894000291824341
topics[1].domain.id	https://openalex.org/domains/2
topics[1].domain.display_name	Social Sciences
topics[1].subfield.id	https://openalex.org/subfields/1804
topics[1].subfield.display_name	Statistics, Probability and Uncertainty
topics[1].display_name	Probabilistic and Robust Engineering Design
topics[2].id	https://openalex.org/T10305
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.9772999882698059
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	Power System Optimization and Stability
is_xpac	False
apc_list.value	3500
apc_list.currency	USD
apc_list.value_usd	3500
apc_paid
concepts[0].id	https://openalex.org/C158622935
concepts[0].level	2
concepts[0].score	0.7418037056922913
concepts[0].wikidata	https://www.wikidata.org/wiki/Q660848
concepts[0].display_name	Nonlinear system
concepts[1].id	https://openalex.org/C50644808
concepts[1].level	2
concepts[1].score	0.6535806655883789
concepts[1].wikidata	https://www.wikidata.org/wiki/Q192776
concepts[1].display_name	Artificial neural network
concepts[2].id	https://openalex.org/C47446073
concepts[2].level	3
concepts[2].score	0.5998489260673523
concepts[2].wikidata	https://www.wikidata.org/wiki/Q5165890
concepts[2].display_name	Control theory (sociology)
concepts[3].id	https://openalex.org/C41008148
concepts[3].level	0
concepts[3].score	0.5800365805625916
concepts[3].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[3].display_name	Computer science
concepts[4].id	https://openalex.org/C108583219
concepts[4].level	2
concepts[4].score	0.4979267120361328
concepts[4].wikidata	https://www.wikidata.org/wiki/Q197536
concepts[4].display_name	Deep learning
concepts[5].id	https://openalex.org/C17020691
concepts[5].level	5
concepts[5].score	0.48552489280700684
concepts[5].wikidata	https://www.wikidata.org/wiki/Q139677
concepts[5].display_name	Operator (biology)
concepts[6].id	https://openalex.org/C122383733
concepts[6].level	2
concepts[6].score	0.4278002977371216
concepts[6].wikidata	https://www.wikidata.org/wiki/Q865920
concepts[6].display_name	Approximation error
concepts[7].id	https://openalex.org/C160824197
concepts[7].level	3
concepts[7].score	0.4209184944629669
concepts[7].wikidata	https://www.wikidata.org/wiki/Q2071054
concepts[7].display_name	Linear approximation
concepts[8].id	https://openalex.org/C2983030100
concepts[8].level	3
concepts[8].score	0.4128061532974243
concepts[8].wikidata	https://www.wikidata.org/wiki/Q638328
concepts[8].display_name	Nonlinear dynamical systems
concepts[9].id	https://openalex.org/C28826006
concepts[9].level	1
concepts[9].score	0.3398344814777374
concepts[9].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[9].display_name	Applied mathematics
concepts[10].id	https://openalex.org/C33923547
concepts[10].level	0
concepts[10].score	0.31745004653930664
concepts[10].wikidata	https://www.wikidata.org/wiki/Q395
concepts[10].display_name	Mathematics
concepts[11].id	https://openalex.org/C11413529
concepts[11].level	1
concepts[11].score	0.30764782428741455
concepts[11].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[11].display_name	Algorithm
concepts[12].id	https://openalex.org/C154945302
concepts[12].level	1
concepts[12].score	0.29336634278297424
concepts[12].wikidata	https://www.wikidata.org/wiki/Q11660
concepts[12].display_name	Artificial intelligence
concepts[13].id	https://openalex.org/C121332964
concepts[13].level	0
concepts[13].score	0.09660902619361877
concepts[13].wikidata	https://www.wikidata.org/wiki/Q413
concepts[13].display_name	Physics
concepts[14].id	https://openalex.org/C2775924081
concepts[14].level	2
concepts[14].score	0.09233322739601135
concepts[14].wikidata	https://www.wikidata.org/wiki/Q55608371
concepts[14].display_name	Control (management)
concepts[15].id	https://openalex.org/C185592680
concepts[15].level	0
concepts[15].score	0.0
concepts[15].wikidata	https://www.wikidata.org/wiki/Q2329
concepts[15].display_name	Chemistry
concepts[16].id	https://openalex.org/C158448853
concepts[16].level	4
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q425218
concepts[16].display_name	Repressor
concepts[17].id	https://openalex.org/C86339819
concepts[17].level	3
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q407384
concepts[17].display_name	Transcription factor
concepts[18].id	https://openalex.org/C104317684
concepts[18].level	2
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q7187
concepts[18].display_name	Gene
concepts[19].id	https://openalex.org/C62520636
concepts[19].level	1
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q944
concepts[19].display_name	Quantum mechanics
concepts[20].id	https://openalex.org/C55493867
concepts[20].level	1
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q7094
concepts[20].display_name	Biochemistry
keywords[0].id	https://openalex.org/keywords/nonlinear-system
keywords[0].score	0.7418037056922913
keywords[0].display_name	Nonlinear system
keywords[1].id	https://openalex.org/keywords/artificial-neural-network
keywords[1].score	0.6535806655883789
keywords[1].display_name	Artificial neural network
keywords[2].id	https://openalex.org/keywords/control-theory
keywords[2].score	0.5998489260673523
keywords[2].display_name	Control theory (sociology)
keywords[3].id	https://openalex.org/keywords/computer-science
keywords[3].score	0.5800365805625916
keywords[3].display_name	Computer science
keywords[4].id	https://openalex.org/keywords/deep-learning
keywords[4].score	0.4979267120361328
keywords[4].display_name	Deep learning
keywords[5].id	https://openalex.org/keywords/operator
keywords[5].score	0.48552489280700684
keywords[5].display_name	Operator (biology)
keywords[6].id	https://openalex.org/keywords/approximation-error
keywords[6].score	0.4278002977371216
keywords[6].display_name	Approximation error
keywords[7].id	https://openalex.org/keywords/linear-approximation
keywords[7].score	0.4209184944629669
keywords[7].display_name	Linear approximation
keywords[8].id	https://openalex.org/keywords/nonlinear-dynamical-systems
keywords[8].score	0.4128061532974243
keywords[8].display_name	Nonlinear dynamical systems
keywords[9].id	https://openalex.org/keywords/applied-mathematics
keywords[9].score	0.3398344814777374
keywords[9].display_name	Applied mathematics
keywords[10].id	https://openalex.org/keywords/mathematics
keywords[10].score	0.31745004653930664
keywords[10].display_name	Mathematics
keywords[11].id	https://openalex.org/keywords/algorithm
keywords[11].score	0.30764782428741455
keywords[11].display_name	Algorithm
keywords[12].id	https://openalex.org/keywords/artificial-intelligence
keywords[12].score	0.29336634278297424
keywords[12].display_name	Artificial intelligence
keywords[13].id	https://openalex.org/keywords/physics
keywords[13].score	0.09660902619361877
keywords[13].display_name	Physics
keywords[14].id	https://openalex.org/keywords/control
keywords[14].score	0.09233322739601135
keywords[14].display_name	Control (management)
language	en
locations[0].id	doi:10.1016/j.automatica.2023.111372
locations[0].is_oa	False
locations[0].source.id	https://openalex.org/S51360982
locations[0].source.issn	0005-1098, 1873-2836
locations[0].source.type	journal
locations[0].source.is_oa	False
locations[0].source.issn_l	0005-1098
locations[0].source.is_core	True
locations[0].source.is_in_doaj	False
locations[0].source.display_name	Automatica
locations[0].source.host_organization	https://openalex.org/P4310320990
locations[0].source.host_organization_name	Elsevier BV
locations[0].source.host_organization_lineage	https://openalex.org/P4310320990
locations[0].source.host_organization_lineage_names	Elsevier BV
locations[0].license
locations[0].pdf_url
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	Automatica
locations[0].landing_page_url	https://doi.org/10.1016/j.automatica.2023.111372
locations[1].id	pmh:oai:osti.gov:2293484
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306402487
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	False
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)
locations[1].source.host_organization	https://openalex.org/I139351228
locations[1].source.host_organization_name	Office of Scientific and Technical Information
locations[1].source.host_organization_lineage	https://openalex.org/I139351228
locations[1].license
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name
locations[1].landing_page_url	https://www.osti.gov/biblio/2293484
indexed_in	crossref
authorships[0].author.id	https://openalex.org/A5030939982
authorships[0].author.orcid
authorships[0].author.display_name	Wenjian Hao
authorships[0].countries	US
authorships[0].affiliations[0].institution_ids	https://openalex.org/I219193219
authorships[0].affiliations[0].raw_affiliation_string	School of Aeronautics and Astronautics, Purdue University, West Lafayette, USA
authorships[0].institutions[0].id	https://openalex.org/I219193219
authorships[0].institutions[0].ror	https://ror.org/02dqehb95
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I219193219
authorships[0].institutions[0].country_code	US
authorships[0].institutions[0].display_name	Purdue University West Lafayette
authorships[0].author_position	first
authorships[0].raw_author_name	Wenjian Hao
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	School of Aeronautics and Astronautics, Purdue University, West Lafayette, USA
authorships[1].author.id	https://openalex.org/A5103278668
authorships[1].author.orcid	https://orcid.org/0000-0003-2339-1123
authorships[1].author.display_name	Bowen Huang
authorships[1].countries	US
authorships[1].affiliations[0].institution_ids	https://openalex.org/I142606810
authorships[1].affiliations[0].raw_affiliation_string	Pacific Northwest National Laboratory, Richland, USA
authorships[1].institutions[0].id	https://openalex.org/I142606810
authorships[1].institutions[0].ror	https://ror.org/05h992307
authorships[1].institutions[0].type	facility
authorships[1].institutions[0].lineage	https://openalex.org/I1325736334, https://openalex.org/I1330989302, https://openalex.org/I142606810, https://openalex.org/I39565521
authorships[1].institutions[0].country_code	US
authorships[1].institutions[0].display_name	Pacific Northwest National Laboratory
authorships[1].author_position	middle
authorships[1].raw_author_name	Bowen Huang
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	Pacific Northwest National Laboratory, Richland, USA
authorships[2].author.id	https://openalex.org/A5100721259
authorships[2].author.orcid	https://orcid.org/0000-0003-1121-9879
authorships[2].author.display_name	Wei Pan
authorships[2].countries	GB
authorships[2].affiliations[0].institution_ids	https://openalex.org/I28407311
authorships[2].affiliations[0].raw_affiliation_string	Department of Computer Science, University of Manchester, UK
authorships[2].institutions[0].id	https://openalex.org/I28407311
authorships[2].institutions[0].ror	https://ror.org/027m9bs27
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I28407311
authorships[2].institutions[0].country_code	GB
authorships[2].institutions[0].display_name	University of Manchester
authorships[2].author_position	middle
authorships[2].raw_author_name	Wei Pan
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Department of Computer Science, University of Manchester, UK
authorships[3].author.id	https://openalex.org/A5100599890
authorships[3].author.orcid	https://orcid.org/0000-0002-4753-8161
authorships[3].author.display_name	Di Wu
authorships[3].countries	US
authorships[3].affiliations[0].institution_ids	https://openalex.org/I142606810
authorships[3].affiliations[0].raw_affiliation_string	Pacific Northwest National Laboratory, Richland, USA
authorships[3].institutions[0].id	https://openalex.org/I142606810
authorships[3].institutions[0].ror	https://ror.org/05h992307
authorships[3].institutions[0].type	facility
authorships[3].institutions[0].lineage	https://openalex.org/I1325736334, https://openalex.org/I1330989302, https://openalex.org/I142606810, https://openalex.org/I39565521
authorships[3].institutions[0].country_code	US
authorships[3].institutions[0].display_name	Pacific Northwest National Laboratory
authorships[3].author_position	middle
authorships[3].raw_author_name	Di Wu
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	Pacific Northwest National Laboratory, Richland, USA
authorships[4].author.id	https://openalex.org/A5070733769
authorships[4].author.orcid	https://orcid.org/0000-0002-3698-4238
authorships[4].author.display_name	Shaoshuai Mou
authorships[4].countries	US
authorships[4].affiliations[0].institution_ids	https://openalex.org/I219193219
authorships[4].affiliations[0].raw_affiliation_string	School of Aeronautics and Astronautics, Purdue University, West Lafayette, USA
authorships[4].institutions[0].id	https://openalex.org/I219193219
authorships[4].institutions[0].ror	https://ror.org/02dqehb95
authorships[4].institutions[0].type	education
authorships[4].institutions[0].lineage	https://openalex.org/I219193219
authorships[4].institutions[0].country_code	US
authorships[4].institutions[0].display_name	Purdue University West Lafayette
authorships[4].author_position	last
authorships[4].raw_author_name	Shaoshuai Mou
authorships[4].is_corresponding	True
authorships[4].raw_affiliation_strings	School of Aeronautics and Astronautics, Purdue University, West Lafayette, USA
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://www.osti.gov/biblio/2293484
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Deep Koopman learning of nonlinear time-varying systems
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T11206
primary_topic.field.id	https://openalex.org/fields/31
primary_topic.field.display_name	Physics and Astronomy
primary_topic.score	1.0
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/3109
primary_topic.subfield.display_name	Statistical and Nonlinear Physics
primary_topic.display_name	Model Reduction and Neural Networks
related_works	https://openalex.org/W2046314839, https://openalex.org/W2037008369, https://openalex.org/W3125388252, https://openalex.org/W652901797, https://openalex.org/W2083813704, https://openalex.org/W2093585199, https://openalex.org/W4311227613, https://openalex.org/W2087686193, https://openalex.org/W2068084037, https://openalex.org/W4282839256
cited_by_count	13
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	11
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	2
locations_count	2
best_oa_location.id	pmh:oai:osti.gov:2293484
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306402487
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	False
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	OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)
best_oa_location.source.host_organization	https://openalex.org/I139351228
best_oa_location.source.host_organization_name	Office of Scientific and Technical Information
best_oa_location.source.host_organization_lineage	https://openalex.org/I139351228
best_oa_location.license
best_oa_location.pdf_url
best_oa_location.version	submittedVersion
best_oa_location.raw_type
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	https://www.osti.gov/biblio/2293484
primary_location.id	doi:10.1016/j.automatica.2023.111372
primary_location.is_oa	False
primary_location.source.id	https://openalex.org/S51360982
primary_location.source.issn	0005-1098, 1873-2836
primary_location.source.type	journal
primary_location.source.is_oa	False
primary_location.source.issn_l	0005-1098
primary_location.source.is_core	True
primary_location.source.is_in_doaj	False
primary_location.source.display_name	Automatica
primary_location.source.host_organization	https://openalex.org/P4310320990
primary_location.source.host_organization_name	Elsevier BV
primary_location.source.host_organization_lineage	https://openalex.org/P4310320990
primary_location.source.host_organization_lineage_names	Elsevier BV
primary_location.license
primary_location.pdf_url
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	Automatica
primary_location.landing_page_url	https://doi.org/10.1016/j.automatica.2023.111372
publication_date	2023-10-21
publication_year	2023
referenced_works	https://openalex.org/W6784603026, https://openalex.org/W2965243272, https://openalex.org/W3081754649, https://openalex.org/W3158127689, https://openalex.org/W3216784117, https://openalex.org/W6772521232, https://openalex.org/W2561027863, https://openalex.org/W2594932112, https://openalex.org/W6744093133, https://openalex.org/W2777417212, https://openalex.org/W3126673178, https://openalex.org/W6713784851, https://openalex.org/W2289725842, https://openalex.org/W2964119648, https://openalex.org/W1998167411, https://openalex.org/W1591018827, https://openalex.org/W6743094116, https://openalex.org/W6792599436, https://openalex.org/W2963006871, https://openalex.org/W3098172061, https://openalex.org/W3100184721, https://openalex.org/W2184811773, https://openalex.org/W1522301498, https://openalex.org/W4200635133, https://openalex.org/W1998441499, https://openalex.org/W3101071828, https://openalex.org/W2751084925
referenced_works_count	27
abstract_inverted_index
cited_by_percentile_year.max	99
cited_by_percentile_year.min	94
corresponding_author_ids	https://openalex.org/A5070733769
countries_distinct_count	2
institutions_distinct_count	5
corresponding_institution_ids	https://openalex.org/I219193219
citation_normalized_percentile.value	0.89785178
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	True