{"id":"https://openalex.org/W4400366221","doi":"https://doi.org/10.1137/23m1602991","title":"Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning","display_name":"Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning","publication_year":2024,"publication_date":"2024-07-05","ids":{"openalex":"https://openalex.org/W4400366221","doi":"https://doi.org/10.1137/23m1602991"},"language":"en","primary_location":{"id":"doi:10.1137/23m1602991","doi":"https://doi.org/10.1137/23m1602991","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1602991","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.07946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050060748","display_name":"Dimitrios G. Patsatzis","orcid":"https://orcid.org/0000-0001-9840-0018","observed_orcids":["https://orcid.org/0000-0001-9840-0018"]},"institutions":[{"id":"https://openalex.org/I4210149489","display_name":"Scuola Superiore Meridionale","ror":"https://ror.org/04swxte59","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210149489"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dimitrios Patsatzis","raw_affiliation_strings":["Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples 80138 Italy"],"raw_orcid":"https://orcid.org/0000-0001-9840-0018","affiliations":[{"raw_affiliation_string":"Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples 80138 Italy","institution_ids":["https://openalex.org/I4210149489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043315604","display_name":"Gianluca Fabiani","orcid":"https://orcid.org/0000-0002-9799-451X","observed_orcids":["https://orcid.org/0000-0002-9799-451X"]},"institutions":[{"id":"https://openalex.org/I4210149489","display_name":"Scuola Superiore Meridionale","ror":"https://ror.org/04swxte59","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210149489"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianluca Fabiani","raw_affiliation_strings":["Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples 80138 Italy"],"raw_orcid":"https://orcid.org/0000-0002-9799-451X","affiliations":[{"raw_affiliation_string":"Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples 80138 Italy","institution_ids":["https://openalex.org/I4210149489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091118133","display_name":"Lucia Russo","orcid":"https://orcid.org/0000-0003-4888-467X","observed_orcids":["https://orcid.org/0000-0003-4888-467X","https://orcid.org/0000-0002-0508-3939"]},"institutions":[{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lucia Russo","raw_affiliation_strings":["Institute of Science and Technology for Energy and Sustainable Mobility (STEMS), Consiglio Nazionale delle Ricerche, Naples 80125 Italy"],"raw_orcid":"https://orcid.org/0000-0003-4888-467X","affiliations":[{"raw_affiliation_string":"Institute of Science and Technology for Energy and Sustainable Mobility (STEMS), Consiglio Nazionale delle Ricerche, Naples 80125 Italy","institution_ids":["https://openalex.org/I4210155236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090389995","display_name":"Constantinos I. Siettos","orcid":"https://orcid.org/0000-0002-9568-3355","observed_orcids":["https://orcid.org/0000-0002-9568-3355"]},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Constantinos Siettos","raw_affiliation_strings":["Dipartimento di Matematica e Applicazioni \u201cRenato Caccioppoli\u201d, Universit\u00e0 degli Studi di Napoli Federico II, Naples 80126 Italy"],"raw_orcid":"https://orcid.org/0000-0002-9568-3355","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Applicazioni \u201cRenato Caccioppoli\u201d, Universit\u00e0 degli Studi di Napoli Federico II, Naples 80126 Italy","institution_ids":["https://openalex.org/I71267560"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0606,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.86791444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"46","issue":"4","first_page":"C297","last_page":"C322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9312000274658203,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9312000274658203,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.06710000336170197,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0005000000237487257,"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/slow-invariant-manifold","display_name":"slow invariant manifold","score":0.9940000176429749},{"id":"https://openalex.org/keywords/slow-fast-systems","display_name":"singularly perturbed systems","score":0.9549999833106995},{"id":"https://openalex.org/keywords/physics-informed-machine-learning","display_name":"physics-informed machine learning","score":0.8859999775886536},{"id":"https://openalex.org/keywords/geometric-singular-perturbation-theory","display_name":"geometric singular perturbation theory","score":0.9210000038146973},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.9079999923706055},{"id":"https://openalex.org/keywords/feedforward-neural-networks","display_name":"feedforward neural networks","score":0.8889999985694885},{"id":"https://openalex.org/keywords/symbolic-differentiation","display_name":"symbolic differentiation","score":0.9419999718666077},{"id":"https://openalex.org/keywords/michaelis-menten-kinetics","display_name":"Michaelis-Menten kinetics","score":0.7870000004768372},{"id":"https://openalex.org/keywords/target-mediated-drug-disposition","display_name":"target-mediated drug disposition","score":0.996999979019165}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5911673903465271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5822927355766296},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.49837684631347656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.440273255109787},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40147170424461365},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3712419271469116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3536941409111023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.294524222612381},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2266121208667755},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.11028638482093811},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/23m1602991","doi":"https://doi.org/10.1137/23m1602991","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1602991","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2309.07946","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.07946","pdf_url":"https://arxiv.org/pdf/2309.07946","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2309.07946","doi":"https://doi.org/10.48550/arxiv.2309.07946","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.07946","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.07946","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.07946","pdf_url":"https://arxiv.org/pdf/2309.07946","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400366221.pdf","grobid_xml":"https://content.openalex.org/works/W4400366221.grobid-xml"},"referenced_works_count":87,"referenced_works":["https://openalex.org/W28215347","https://openalex.org/W99189181","https://openalex.org/W152317225","https://openalex.org/W420509224","https://openalex.org/W568989277","https://openalex.org/W947716554","https://openalex.org/W1591018827","https://openalex.org/W1687850508","https://openalex.org/W1938657618","https://openalex.org/W1964440321","https://openalex.org/W1966113499","https://openalex.org/W1968501759","https://openalex.org/W1985205248","https://openalex.org/W1986278072","https://openalex.org/W1991418841","https://openalex.org/W1996640396","https://openalex.org/W1997508985","https://openalex.org/W1998280858","https://openalex.org/W2001698066","https://openalex.org/W2002164453","https://openalex.org/W2004094140","https://openalex.org/W2006002535","https://openalex.org/W2006554089","https://openalex.org/W2012030128","https://openalex.org/W2016767879","https://openalex.org/W2019685954","https://openalex.org/W2024972590","https://openalex.org/W2025475039","https://openalex.org/W2032227660","https://openalex.org/W2035502912","https://openalex.org/W2039616943","https://openalex.org/W2041210714","https://openalex.org/W2043908043","https://openalex.org/W2044359900","https://openalex.org/W2053186076","https://openalex.org/W2064668598","https://openalex.org/W2070460788","https://openalex.org/W2086387602","https://openalex.org/W2086709230","https://openalex.org/W2090950392","https://openalex.org/W2093402979","https://openalex.org/W2095889937","https://openalex.org/W2097892506","https://openalex.org/W2103496339","https://openalex.org/W2106566376","https://openalex.org/W2110841752","https://openalex.org/W2111072639","https://openalex.org/W2134118243","https://openalex.org/W2138278836","https://openalex.org/W2141906015","https://openalex.org/W2155482699","https://openalex.org/W2161317287","https://openalex.org/W2166116275","https://openalex.org/W2413977353","https://openalex.org/W2471063652","https://openalex.org/W2572805213","https://openalex.org/W2595897327","https://openalex.org/W2776928020","https://openalex.org/W2777417212","https://openalex.org/W2781487518","https://openalex.org/W2898436200","https://openalex.org/W2899283552","https://openalex.org/W2938226738","https://openalex.org/W2956013039","https://openalex.org/W2957969499","https://openalex.org/W2999271947","https://openalex.org/W3002310157","https://openalex.org/W3008606610","https://openalex.org/W3107426801","https://openalex.org/W3110987241","https://openalex.org/W3112440564","https://openalex.org/W3137611682","https://openalex.org/W3155529179","https://openalex.org/W3163993681","https://openalex.org/W3178264488","https://openalex.org/W3205549933","https://openalex.org/W3215875127","https://openalex.org/W4221156459","https://openalex.org/W4226329567","https://openalex.org/W4236765228","https://openalex.org/W4280647708","https://openalex.org/W4283359998","https://openalex.org/W4290672252","https://openalex.org/W4315628777","https://openalex.org/W4318269846","https://openalex.org/W4381470412","https://openalex.org/W4383872025"],"related_works":["https://openalex.org/W4405334206","https://openalex.org/W2972235247","https://openalex.org/W4410436197","https://openalex.org/W7124734168","https://openalex.org/W7097918023","https://openalex.org/W4415311325","https://openalex.org/W4410430137","https://openalex.org/W2032227660","https://openalex.org/W4387276520","https://openalex.org/W7099052899"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,120],"present":[2],"a":[3,231],"physics-informed":[4],"machine":[5],"learning":[6,92,208],"(PIML)":[7],"approach":[8],"for":[9,83,90,145,170],"the":[10,28,41,47,52,60,63,84,87,91,107,109,116,123,154,157,172,175,193,203,207,222,234,244,256],"approximation":[11,201],"of":[12,16,33,62,86,96,129,156,162,192,202,214],"slow":[13,178],"invariant":[14],"manifolds":[15],"singularly":[17],"perturbed":[18],"systems,":[19],"providing":[20],"functionals":[21],"in":[22,206,258],"an":[23],"explicit":[24],"form":[25],"that":[26,122,182,233,251],"facilitates":[27],"construction":[29],"and":[30,75,115,143,177,199,227,243,249,265],"numerical":[31,200],"integration":[32],"reduced-order":[34],"models":[35],"(ROMs).":[36],"The":[37,94],"proposed":[38,124],"scheme":[39,126],"solves":[40],"partial":[42],"differential":[43],"equation":[44,49],"corresponding":[45],"to":[46,254],"invariance":[48],"(IE)":[50],"within":[51],"geometric":[53],"singular":[54],"perturbation":[55,158],"theory":[56],"(GSPT)":[57],"framework.":[58],"For":[59],"solution":[61],"IE,":[64],"we":[65],"used":[66],"two":[67],"neural":[68,73,78],"network":[69],"structures,":[70],"namely,":[71,106],"feedforward":[72],"networks":[74],"random":[76],"projection":[77],"networks,":[79],"with":[80],"symbolic":[81],"differentiation":[82],"computation":[85],"gradients":[88],"required":[89,204],"process.":[93],"efficiency":[95],"our":[97],"PIML":[98,125],"method":[99],"is":[100,150,161,180,210],"assessed":[101],"via":[102],"three":[103],"benchmark":[104],"problems,":[105],"Michaelis\u2013Menten,":[108],"target-mediated":[110],"drug":[111],"disposition":[112],"reaction":[113],"mechanism,":[114],"3D":[117],"Sel\u2019kov":[118],"model.":[119],"show":[121],"provides":[127],"approximations":[128],"equivalent":[130],"or":[131],"even":[132],"higher":[133],"accuracy":[134],"than":[135],"those":[136],"provided":[137],"by":[138,153,241],"other":[139],"traditional":[140],"GSPT-based":[141],"methods,":[142],"importantly,":[144],"any":[146],"practical":[147],"purposes,":[148],"it":[149],"not":[151,181],"affected":[152],"magnitude":[155],"parameter.":[159],"This":[160,217],"particular":[163],"importance":[164],"because":[165],"there":[166],"are":[167,261],"many":[168],"systems":[169],"which":[171],"gap":[173],"between":[174,196],"fast":[176],"timescales":[179],"big,":[183],"but":[184],"still,":[185],"ROMs":[186],"can":[187],"be":[188],"constructed.":[189],"A":[190],"comparison":[191],"computational":[194,215],"costs":[195],"symbolic,":[197],"automatic,":[198],"derivatives":[205],"process":[209],"also":[211],"provided.":[212],"Reproducibility":[213,224],"results.":[216],"paper":[218,260],"has":[219],"been":[220],"awarded":[221],"\u201cSIAM":[223],"Badge:":[225],"Code":[226,248],"data":[228,250],"available\u201d":[229],"as":[230],"recognition":[232],"authors":[235],"have":[236],"followed":[237],"reproducibility":[238],"principles":[239],"valued":[240],"SISC":[242],"scientific":[245],"computing":[246],"community.":[247],"allow":[252],"readers":[253],"reproduce":[255],"results":[257],"this":[259],"available":[262],"at":[263],"https://epubs.siam.org/doi/suppl/10.1137/23M1602991/suppl_file/131735_1_supp_551502_s5k7wy_sc.pdf":[264],"https://epubs.siam.org/doi/suppl/10.1137/23M1602991/suppl_file/SISC_PIML_SIMs_SP-main.zip":[266],".":[267],"[Formula:":[268],"see":[269],"text]":[270]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2024-07-06T00:00:00"}