A new perspective on dynamic network flow problems via port-Hamiltonian systems Article Swipe

PDF

Onur Tanil Doganay , Kathrin Klamroth , Bruno Lang , Michael Stiglmayr , Claudia Totzeck ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2303.15082

We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general port-Hamiltonian systems with possibly state-dependent system matrices. We prove well-posedness of these systems and characterize optimal controls by the first-order optimality system, which is the starting point for the derivation of an adjoint-based gradient descent algorithm. Our theoretical analysis is complemented by a proof of concept, where we apply the proposed algorithm to static minimum cost flow problems and dynamic minimum cost flow problems on a simple directed acyclic graph. We present numerical results to validate the approach.

Related Topics

Mathematical Analysis

Electrical Engineering

Geometry

Engineering

Machine Learning

Concepts

Balanced flow Hamiltonian (control theory) Minimum-cost flow problem Flow network Mathematical optimization Mathematics Port (circuit theory) Gradient descent Hamiltonian system Graph Directed graph Computer science Optimal control Flow (mathematics) Algorithm Discrete mathematics Mathematical analysis Electrical engineering Geometry Artificial neural network Engineering Machine learning

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2303.15082
PDF: https://arxiv.org/pdf/2303.15082
OA Status: green
Cited By: 1
Related Works: 10
OpenAlex ID: https://openalex.org/W4361193876

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4361193876

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2303.15082

Digital Object Identifier
Title: A new perspective on dynamic network flow problems via port-Hamiltonian systems

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-03-27

Full publication date if available
Authors: Onur Tanil Doganay, Kathrin Klamroth, Bruno Lang, Michael Stiglmayr, Claudia Totzeck

List of authors in order
Landing page: https://arxiv.org/abs/2303.15082

Publisher landing page
PDF URL: https://arxiv.org/pdf/2303.15082

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/2303.15082

Direct OA link when available
Concepts: Balanced flow, Hamiltonian (control theory), Minimum-cost flow problem, Flow network, Mathematical optimization, Mathematics, Port (circuit theory), Gradient descent, Hamiltonian system, Graph, Directed graph, Computer science, Optimal control, Flow (mathematics), Algorithm, Discrete mathematics, Mathematical analysis, Electrical engineering, Geometry, Artificial neural network, Engineering, Machine learning

Top concepts (fields/topics) attached by OpenAlex
Cited by: 1

Total citation count in OpenAlex
Citations by year (recent): 2025: 1

Per-year citation counts (last 5 years)
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4361193876
doi	https://doi.org/10.48550/arxiv.2303.15082
ids.doi	https://doi.org/10.48550/arxiv.2303.15082
ids.openalex	https://openalex.org/W4361193876
fwci
type	preprint
title	A new perspective on dynamic network flow problems via port-Hamiltonian systems
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10612
topics[0].field.id	https://openalex.org/fields/25
topics[0].field.display_name	Materials Science
topics[0].score	0.9699000120162964
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2504
topics[0].subfield.display_name	Electronic, Optical and Magnetic Materials
topics[0].display_name	Magnetism in coordination complexes
topics[1].id	https://openalex.org/T12772
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.965499997138977
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2207
topics[1].subfield.display_name	Control and Systems Engineering
topics[1].display_name	Control and Stability of Dynamical Systems
topics[2].id	https://openalex.org/T10792
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.9573000073432922
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1703
topics[2].subfield.display_name	Computational Theory and Mathematics
topics[2].display_name	Matrix Theory and Algorithms
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C167879884
concepts[0].level	2
concepts[0].score	0.7051021456718445
concepts[0].wikidata	https://www.wikidata.org/wiki/Q727568
concepts[0].display_name	Balanced flow
concepts[1].id	https://openalex.org/C130787639
concepts[1].level	2
concepts[1].score	0.5951465368270874
concepts[1].wikidata	https://www.wikidata.org/wiki/Q5645293
concepts[1].display_name	Hamiltonian (control theory)
concepts[2].id	https://openalex.org/C99545648
concepts[2].level	3
concepts[2].score	0.5875405669212341
concepts[2].wikidata	https://www.wikidata.org/wiki/Q2897180
concepts[2].display_name	Minimum-cost flow problem
concepts[3].id	https://openalex.org/C114809511
concepts[3].level	2
concepts[3].score	0.5442782044410706
concepts[3].wikidata	https://www.wikidata.org/wiki/Q1412924
concepts[3].display_name	Flow network
concepts[4].id	https://openalex.org/C126255220
concepts[4].level	1
concepts[4].score	0.540148913860321
concepts[4].wikidata	https://www.wikidata.org/wiki/Q141495
concepts[4].display_name	Mathematical optimization
concepts[5].id	https://openalex.org/C33923547
concepts[5].level	0
concepts[5].score	0.5146639943122864
concepts[5].wikidata	https://www.wikidata.org/wiki/Q395
concepts[5].display_name	Mathematics
concepts[6].id	https://openalex.org/C32802771
concepts[6].level	2
concepts[6].score	0.49015507102012634
concepts[6].wikidata	https://www.wikidata.org/wiki/Q2443617
concepts[6].display_name	Port (circuit theory)
concepts[7].id	https://openalex.org/C153258448
concepts[7].level	3
concepts[7].score	0.4741377532482147
concepts[7].wikidata	https://www.wikidata.org/wiki/Q1199743
concepts[7].display_name	Gradient descent
concepts[8].id	https://openalex.org/C121770821
concepts[8].level	2
concepts[8].score	0.4345250427722931
concepts[8].wikidata	https://www.wikidata.org/wiki/Q2072471
concepts[8].display_name	Hamiltonian system
concepts[9].id	https://openalex.org/C132525143
concepts[9].level	2
concepts[9].score	0.43166467547416687
concepts[9].wikidata	https://www.wikidata.org/wiki/Q141488
concepts[9].display_name	Graph
concepts[10].id	https://openalex.org/C146380142
concepts[10].level	2
concepts[10].score	0.42942094802856445
concepts[10].wikidata	https://www.wikidata.org/wiki/Q1137726
concepts[10].display_name	Directed graph
concepts[11].id	https://openalex.org/C41008148
concepts[11].level	0
concepts[11].score	0.42829272150993347
concepts[11].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[11].display_name	Computer science
concepts[12].id	https://openalex.org/C91575142
concepts[12].level	2
concepts[12].score	0.421242356300354
concepts[12].wikidata	https://www.wikidata.org/wiki/Q1971426
concepts[12].display_name	Optimal control
concepts[13].id	https://openalex.org/C38349280
concepts[13].level	2
concepts[13].score	0.4142639636993408
concepts[13].wikidata	https://www.wikidata.org/wiki/Q1434290
concepts[13].display_name	Flow (mathematics)
concepts[14].id	https://openalex.org/C11413529
concepts[14].level	1
concepts[14].score	0.2580792307853699
concepts[14].wikidata	https://www.wikidata.org/wiki/Q8366
concepts[14].display_name	Algorithm
concepts[15].id	https://openalex.org/C118615104
concepts[15].level	1
concepts[15].score	0.13638582825660706
concepts[15].wikidata	https://www.wikidata.org/wiki/Q121416
concepts[15].display_name	Discrete mathematics
concepts[16].id	https://openalex.org/C134306372
concepts[16].level	1
concepts[16].score	0.08763700723648071
concepts[16].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[16].display_name	Mathematical analysis
concepts[17].id	https://openalex.org/C119599485
concepts[17].level	1
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q43035
concepts[17].display_name	Electrical engineering
concepts[18].id	https://openalex.org/C2524010
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[18].display_name	Geometry
concepts[19].id	https://openalex.org/C50644808
concepts[19].level	2
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q192776
concepts[19].display_name	Artificial neural network
concepts[20].id	https://openalex.org/C127413603
concepts[20].level	0
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q11023
concepts[20].display_name	Engineering
concepts[21].id	https://openalex.org/C119857082
concepts[21].level	1
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q2539
concepts[21].display_name	Machine learning
keywords[0].id	https://openalex.org/keywords/balanced-flow
keywords[0].score	0.7051021456718445
keywords[0].display_name	Balanced flow
keywords[1].id	https://openalex.org/keywords/hamiltonian
keywords[1].score	0.5951465368270874
keywords[1].display_name	Hamiltonian (control theory)
keywords[2].id	https://openalex.org/keywords/minimum-cost-flow-problem
keywords[2].score	0.5875405669212341
keywords[2].display_name	Minimum-cost flow problem
keywords[3].id	https://openalex.org/keywords/flow-network
keywords[3].score	0.5442782044410706
keywords[3].display_name	Flow network
keywords[4].id	https://openalex.org/keywords/mathematical-optimization
keywords[4].score	0.540148913860321
keywords[4].display_name	Mathematical optimization
keywords[5].id	https://openalex.org/keywords/mathematics
keywords[5].score	0.5146639943122864
keywords[5].display_name	Mathematics
keywords[6].id	https://openalex.org/keywords/port
keywords[6].score	0.49015507102012634
keywords[6].display_name	Port (circuit theory)
keywords[7].id	https://openalex.org/keywords/gradient-descent
keywords[7].score	0.4741377532482147
keywords[7].display_name	Gradient descent
keywords[8].id	https://openalex.org/keywords/hamiltonian-system
keywords[8].score	0.4345250427722931
keywords[8].display_name	Hamiltonian system
keywords[9].id	https://openalex.org/keywords/graph
keywords[9].score	0.43166467547416687
keywords[9].display_name	Graph
keywords[10].id	https://openalex.org/keywords/directed-graph
keywords[10].score	0.42942094802856445
keywords[10].display_name	Directed graph
keywords[11].id	https://openalex.org/keywords/computer-science
keywords[11].score	0.42829272150993347
keywords[11].display_name	Computer science
keywords[12].id	https://openalex.org/keywords/optimal-control
keywords[12].score	0.421242356300354
keywords[12].display_name	Optimal control
keywords[13].id	https://openalex.org/keywords/flow
keywords[13].score	0.4142639636993408
keywords[13].display_name	Flow (mathematics)
keywords[14].id	https://openalex.org/keywords/algorithm
keywords[14].score	0.2580792307853699
keywords[14].display_name	Algorithm
keywords[15].id	https://openalex.org/keywords/discrete-mathematics
keywords[15].score	0.13638582825660706
keywords[15].display_name	Discrete mathematics
keywords[16].id	https://openalex.org/keywords/mathematical-analysis
keywords[16].score	0.08763700723648071
keywords[16].display_name	Mathematical analysis
language	en
locations[0].id	pmh:oai:arXiv.org:2303.15082
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
locations[0].pdf_url	https://arxiv.org/pdf/2303.15082
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2303.15082
locations[1].id	doi:10.48550/arxiv.2303.15082
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.2303.15082
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5028262657
authorships[0].author.orcid
authorships[0].author.display_name	Onur Tanil Doganay
authorships[0].author_position	first
authorships[0].raw_author_name	Doganay, Onur Tanil
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5056075291
authorships[1].author.orcid	https://orcid.org/0000-0001-9119-0732
authorships[1].author.display_name	Kathrin Klamroth
authorships[1].author_position	middle
authorships[1].raw_author_name	Klamroth, Kathrin
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5070913387
authorships[2].author.orcid	https://orcid.org/0000-0001-9197-4836
authorships[2].author.display_name	Bruno Lang
authorships[2].author_position	middle
authorships[2].raw_author_name	Lang, Bruno
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5064817215
authorships[3].author.orcid	https://orcid.org/0000-0003-0926-1584
authorships[3].author.display_name	Michael Stiglmayr
authorships[3].author_position	middle
authorships[3].raw_author_name	Stiglmayr, Michael
authorships[3].is_corresponding	False
authorships[4].author.id	https://openalex.org/A5045326930
authorships[4].author.orcid	https://orcid.org/0000-0001-6283-7154
authorships[4].author.display_name	Claudia Totzeck
authorships[4].author_position	last
authorships[4].raw_author_name	Totzeck, Claudia
authorships[4].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2303.15082
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2023-03-31T00:00:00
display_name	A new perspective on dynamic network flow problems via port-Hamiltonian systems
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10612
primary_topic.field.id	https://openalex.org/fields/25
primary_topic.field.display_name	Materials Science
primary_topic.score	0.9699000120162964
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2504
primary_topic.subfield.display_name	Electronic, Optical and Magnetic Materials
primary_topic.display_name	Magnetism in coordination complexes
related_works	https://openalex.org/W3141113327, https://openalex.org/W2080904092, https://openalex.org/W3035974271, https://openalex.org/W3161514703, https://openalex.org/W3207627914, https://openalex.org/W2270959725, https://openalex.org/W2151525839, https://openalex.org/W648253840, https://openalex.org/W2051329268, https://openalex.org/W2092572272
cited_by_count	1
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	1
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2303.15082
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
best_oa_location.pdf_url	https://arxiv.org/pdf/2303.15082
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
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	http://arxiv.org/abs/2303.15082
primary_location.id	pmh:oai:arXiv.org:2303.15082
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
primary_location.pdf_url	https://arxiv.org/pdf/2303.15082
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2303.15082
publication_date	2023-03-27
publication_year	2023
referenced_works_count	0
abstract_inverted_index.a	2, 75, 98
abstract_inverted_index.We	0, 40, 103
abstract_inverted_index.an	64
abstract_inverted_index.as	26
abstract_inverted_index.by	50, 74
abstract_inverted_index.is	56, 72
abstract_inverted_index.of	13, 43, 63, 77
abstract_inverted_index.on	5, 97
abstract_inverted_index.to	16, 85, 107
abstract_inverted_index.we	80
abstract_inverted_index.Our	69
abstract_inverted_index.and	46, 91
abstract_inverted_index.are	24
abstract_inverted_index.for	31, 60
abstract_inverted_index.the	14, 51, 57, 61, 82, 109
abstract_inverted_index.cost	21, 88, 94
abstract_inverted_index.flow	8, 22, 89, 95
abstract_inverted_index.that	10
abstract_inverted_index.with	35
abstract_inverted_index.apply	81
abstract_inverted_index.point	59
abstract_inverted_index.proof	76
abstract_inverted_index.prove	41
abstract_inverted_index.takes	11
abstract_inverted_index.these	44
abstract_inverted_index.where	79
abstract_inverted_index.which	55
abstract_inverted_index.global	3
abstract_inverted_index.graph.	102
abstract_inverted_index.simple	99
abstract_inverted_index.static	86
abstract_inverted_index.system	38
abstract_inverted_index.Dynamic	19
abstract_inverted_index.acyclic	101
abstract_inverted_index.control	29
abstract_inverted_index.descent	67
abstract_inverted_index.dynamic	6, 92
abstract_inverted_index.general	32
abstract_inverted_index.minimum	20, 87, 93
abstract_inverted_index.network	7
abstract_inverted_index.optimal	28, 48
abstract_inverted_index.present	104
abstract_inverted_index.results	106
abstract_inverted_index.suggest	1
abstract_inverted_index.system,	54
abstract_inverted_index.systems	34, 45
abstract_inverted_index.analysis	71
abstract_inverted_index.concept,	78
abstract_inverted_index.controls	49
abstract_inverted_index.directed	100
abstract_inverted_index.gradient	66
abstract_inverted_index.possibly	36
abstract_inverted_index.problems	9, 23, 30, 90, 96
abstract_inverted_index.proposed	83
abstract_inverted_index.starting	58
abstract_inverted_index.validate	108
abstract_inverted_index.advantage	12
abstract_inverted_index.algorithm	84
abstract_inverted_index.approach.	110
abstract_inverted_index.dynamics.	18
abstract_inverted_index.matrices.	39
abstract_inverted_index.numerical	105
abstract_inverted_index.open-loop	27
abstract_inverted_index.algorithm.	68
abstract_inverted_index.derivation	62
abstract_inverted_index.formulated	25
abstract_inverted_index.optimality	53
abstract_inverted_index.first-order	52
abstract_inverted_index.perspective	4
abstract_inverted_index.theoretical	70
abstract_inverted_index.characterize	47
abstract_inverted_index.complemented	73
abstract_inverted_index.similarities	15
abstract_inverted_index.adjoint-based	65
abstract_inverted_index.well-posedness	42
abstract_inverted_index.state-dependent	37
abstract_inverted_index.port-Hamiltonian	17, 33
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	5
citation_normalized_percentile