{"id":"https://openalex.org/W4293399525","doi":"https://doi.org/10.1007/978-3-031-15839-1_15","title":"Reachability Analysis of\u00a0a\u00a0General Class of\u00a0Neural Ordinary Differential Equations","display_name":"Reachability Analysis of\u00a0a\u00a0General Class of\u00a0Neural Ordinary Differential Equations","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4293399525","doi":"https://doi.org/10.1007/978-3-031-15839-1_15"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-15839-1_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15839-1_15","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021939745","display_name":"Diego Manzanas Lopez","orcid":"https://orcid.org/0000-0003-0721-1241"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Diego Manzanas Lopez","raw_affiliation_strings":["Vanderbilt University, Nashville, TN, 37212, USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University, Nashville, TN, 37212, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056925300","display_name":"Patrick Musau","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick Musau","raw_affiliation_strings":["Vanderbilt University, Nashville, TN, 37212, USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University, Nashville, TN, 37212, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062691664","display_name":"Nathaniel Hamilton","orcid":"https://orcid.org/0000-0002-7147-1964"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathaniel P. Hamilton","raw_affiliation_strings":["Vanderbilt University, Nashville, TN, 37212, USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University, Nashville, TN, 37212, USA","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067901159","display_name":"Taylor T. Johnson","orcid":"https://orcid.org/0000-0001-8021-9923"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Taylor T. Johnson","raw_affiliation_strings":["Vanderbilt University, Nashville, TN, 37212, USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University, Nashville, TN, 37212, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021939745"],"corresponding_institution_ids":["https://openalex.org/I200719446"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.4574,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.95474742,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"258","last_page":"277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11178","display_name":"Receptor Mechanisms and Signaling","score":0.9373000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.8992307186126709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7789602875709534},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7380465269088745},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7051175832748413},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.69932621717453},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5231313109397888},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4786226153373718},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.44006386399269104},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.4235784113407135},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4183924198150635},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38535526394844055},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3693046569824219},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.31078529357910156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.19758746027946472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15715324878692627},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12924528121948242}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8992307186126709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7789602875709534},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7380465269088745},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7051175832748413},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.69932621717453},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5231313109397888},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4786226153373718},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.44006386399269104},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.4235784113407135},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4183924198150635},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38535526394844055},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3693046569824219},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.31078529357910156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.19758746027946472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15715324878692627},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12924528121948242},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-15839-1_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15839-1_15","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W172589331","https://openalex.org/W1981276685","https://openalex.org/W2015863039","https://openalex.org/W2176215692","https://openalex.org/W2594877703","https://openalex.org/W2734705105","https://openalex.org/W2800473699","https://openalex.org/W2803699674","https://openalex.org/W2898878200","https://openalex.org/W2919694184","https://openalex.org/W2938701611","https://openalex.org/W2948180708","https://openalex.org/W2957311447","https://openalex.org/W2963054787","https://openalex.org/W2964130946","https://openalex.org/W2965543245","https://openalex.org/W2974147052","https://openalex.org/W2980176594","https://openalex.org/W2980176926","https://openalex.org/W3011864700","https://openalex.org/W3021958118","https://openalex.org/W3046272654","https://openalex.org/W3046662910","https://openalex.org/W3080908617","https://openalex.org/W3091798065","https://openalex.org/W3098560806","https://openalex.org/W3112385784","https://openalex.org/W3120214687","https://openalex.org/W3124237877","https://openalex.org/W3160641830","https://openalex.org/W3184441520","https://openalex.org/W3199281236","https://openalex.org/W3201037672","https://openalex.org/W4200164757","https://openalex.org/W4205950066","https://openalex.org/W4283820925","https://openalex.org/W4285597864"],"related_works":["https://openalex.org/W2357387646","https://openalex.org/W856973001","https://openalex.org/W2047831585","https://openalex.org/W4253760428","https://openalex.org/W2099490078","https://openalex.org/W2952920810","https://openalex.org/W4293477811","https://openalex.org/W2017676950","https://openalex.org/W78063724","https://openalex.org/W197679583"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}