{"id":"https://openalex.org/W4385435120","doi":"https://doi.org/10.1007/978-3-031-38271-0_7","title":"Functional Properties of\u00a0PDE-Based Group Equivariant Convolutional Neural Networks","display_name":"Functional Properties of\u00a0PDE-Based Group Equivariant Convolutional Neural Networks","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4385435120","doi":"https://doi.org/10.1007/978-3-031-38271-0_7"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-38271-0_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-38271-0_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.tue.nl/ws/files/346770602/978-3-031-38271-0_7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061936986","display_name":"Gautam Pai","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Gautam Pai","raw_affiliation_strings":["Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074897113","display_name":"Gijs Bellaard","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Gijs Bellaard","raw_affiliation_strings":["Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103105299","display_name":"Bart Smets","orcid":"https://orcid.org/0000-0001-8480-0782"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bart M. N. Smets","raw_affiliation_strings":["Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013378425","display_name":"Remco Duits","orcid":"https://orcid.org/0000-0001-8910-3695"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Remco Duits","raw_affiliation_strings":["Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Center for Analysis, Scientific Computing and Applications, (Group: Geometric Learning and Differential Geometry), Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061936986"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.9886,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.91324748,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"63","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12859","display_name":"Cell Image Analysis Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.9157328605651855},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.7105528116226196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7007570266723633},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6831032633781433},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5842929482460022},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5712327361106873},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4861278533935547},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4384458661079407},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.424709290266037},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.42308345437049866},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.4212946593761444},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3487021327018738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2655319571495056},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22869980335235596},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13405868411064148},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10046717524528503}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.9157328605651855},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.7105528116226196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7007570266723633},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6831032633781433},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5842929482460022},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5712327361106873},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4861278533935547},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4384458661079407},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.424709290266037},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.42308345437049866},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.4212946593761444},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3487021327018738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2655319571495056},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22869980335235596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13405868411064148},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10046717524528503},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-031-38271-0_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-38271-0_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.tue.nl:publications/1ac0b016-0566-4de7-acc7-26f5586c5756","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/1ac0b016-0566-4de7-acc7-26f5586c5756","pdf_url":"https://pure.tue.nl/ws/files/346770602/978-3-031-38271-0_7.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pai, G, Bellaard, G, Smets, B M N & Duits, R 2023, Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks. in F Nielsen & F Barbaresco (eds), Geometric Science of Information : 6th International Conference, GSI 2023, St. Malo, France, August 30 \u2013 September 1, 2023, Proceedings, Part I. Lecture Notes in Computer Science (LNCS), vol. 14071, Springer, Cham, pp. 63\u201372, 6th International Conference on Geometric Science of Information, GSI 2023, St. Malo, France, 30/08/23. https://doi.org/10.1007/978-3-031-38271-0_7","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/1ac0b016-0566-4de7-acc7-26f5586c5756","is_oa":true,"landing_page_url":"https://research.tue.nl/files/346770602/978-3-031-38271-0_7.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pai, G, Bellaard, G, Smets, B M N & Duits, R 2023, Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks. in F Nielsen & F Barbaresco (eds), Geometric Science of Information : 6th International Conference, GSI 2023, St. Malo, France, August 30 \u2013 September 1, 2023, Proceedings, Part I. Lecture Notes in Computer Science (LNCS), vol. 14071, Springer, Cham, pp. 63\u201372, 6th International Conference on Geometric Science of Information, GSI 2023, St. Malo, France, 30/08/23. https://doi.org/10.1007/978-3-031-38271-0_7","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:publications/1ac0b016-0566-4de7-acc7-26f5586c5756","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/1ac0b016-0566-4de7-acc7-26f5586c5756","pdf_url":"https://pure.tue.nl/ws/files/346770602/978-3-031-38271-0_7.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pai, G, Bellaard, G, Smets, B M N & Duits, R 2023, Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks. in F Nielsen & F Barbaresco (eds), Geometric Science of Information : 6th International Conference, GSI 2023, St. Malo, France, August 30 \u2013 September 1, 2023, Proceedings, Part I. Lecture Notes in Computer Science (LNCS), vol. 14071, Springer, Cham, pp. 63\u201372, 6th International Conference on Geometric Science of Information, GSI 2023, St. Malo, France, 30/08/23. https://doi.org/10.1007/978-3-031-38271-0_7","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6981362381","display_name":null,"funder_award_id":"VICI 2020","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385435120.pdf","grobid_xml":"https://content.openalex.org/works/W4385435120.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1901129140","https://openalex.org/W2001412060","https://openalex.org/W2064160177","https://openalex.org/W2081720765","https://openalex.org/W2093193798","https://openalex.org/W2096992873","https://openalex.org/W2142643841","https://openalex.org/W2167383966","https://openalex.org/W2314964624","https://openalex.org/W2963343946","https://openalex.org/W2996594166","https://openalex.org/W3001808426","https://openalex.org/W3110161570","https://openalex.org/W3148563252","https://openalex.org/W3159319455","https://openalex.org/W3165455669","https://openalex.org/W4232499108","https://openalex.org/W4366003524","https://openalex.org/W4376456327"],"related_works":["https://openalex.org/W3148895720","https://openalex.org/W2393913406","https://openalex.org/W30258475","https://openalex.org/W2356579025","https://openalex.org/W2736697936","https://openalex.org/W3211835374","https://openalex.org/W2548611373","https://openalex.org/W1601809778","https://openalex.org/W3169304289","https://openalex.org/W2373733345"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}