{"id":"https://openalex.org/W7128638380","doi":"https://doi.org/10.48550/arxiv.2602.09980","title":"Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks","display_name":"Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128638380","doi":"https://doi.org/10.48550/arxiv.2602.09980"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.09980","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120283638","display_name":"Enzo Nicol\u00e1s Spotorno","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Spotorno, Enzo Nicolas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125673968","display_name":"Josafat Ribeiro Leal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leal, Josafat Ribeiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125659105","display_name":"Antonio Augusto Frohlich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frohlich, Antonio Augusto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19437719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9642999768257141,"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":0.9642999768257141,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.013199999928474426,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6060000061988831},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5432000160217285},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5062999725341797},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4896000027656555},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.43549999594688416},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3797000050544739},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.3666999936103821},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.362199991941452}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6060000061988831},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5062999725341797},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5037999749183655},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4896000027656555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4756999909877777},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3878999948501587},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.32600000500679016},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2879999876022339},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2727999985218048},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.09980","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.09980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09980","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.09980","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Standard":[0],"Physics-Informed":[1],"Neural":[2],"Networks":[3],"(PINNs)":[4],"often":[5],"face":[6],"challenges":[7],"when":[8],"modeling":[9],"parameterized":[10],"dynamical":[11],"systems":[12],"with":[13,152],"sharp":[14],"regime":[15],"transitions,":[16],"such":[17],"as":[18],"bifurcations.":[19],"In":[20],"these":[21],"scenarios,":[22],"the":[23,39,59,80,89,118,126],"continuous":[24],"mapping":[25],"from":[26,135],"parameters":[27,73,166],"to":[28,53,75,87,113],"solutions":[29],"can":[30],"result":[31],"in":[32],"spectral":[33,136],"bias":[34,137],"or":[35],"\"mode":[36],"collapse\",":[37],"where":[38],"network":[40],"averages":[41],"distinct":[42],"physical":[43,72],"behaviors.":[44],"We":[45,102],"propose":[46],"a":[47,83,107,158,168],"Topology-Aware":[48],"PINN":[49],"(TAPINN)":[50],"that":[51,70,130],"aims":[52],"mitigate":[54],"this":[55,104],"challenge":[56],"by":[57],"structuring":[58],"latent":[60,84],"space":[61],"via":[62],"Supervised":[63],"Metric":[64],"Regularization.":[65],"Unlike":[66],"standard":[67,132],"parametric":[68],"PINNs":[69],"map":[71],"directly":[74],"solutions,":[76],"our":[77,147],"method":[78],"conditions":[79],"solver":[81],"on":[82,125],"state":[85],"optimized":[86],"reflect":[88],"metric-based":[90],"separation":[91],"between":[92,117],"regimes,":[93],"showing":[94],"~49%":[95],"lower":[96,154],"physics":[97,121],"residual":[98],"(0.082":[99],"vs.":[100],"0.160).":[101],"train":[103],"architecture":[105],"using":[106],"phase-based":[108],"Alternating":[109],"Optimization":[110],"(AO)":[111],"schedule":[112],"manage":[114],"gradient":[115,155],"conflicts":[116],"metric":[119],"and":[120,138,163],"objectives.":[122],"Preliminary":[123],"experiments":[124],"Duffing":[127],"Oscillator":[128],"demonstrate":[129],"while":[131,144],"baselines":[133],"suffer":[134],"high-capacity":[139],"Hypernetworks":[140],"overfit":[141],"(memorizing":[142],"data":[143],"violating":[145],"physics),":[146],"approach":[148],"achieves":[149],"stable":[150],"convergence":[151],"2.18x":[153],"variance":[156],"than":[157,167],"multi-output":[159],"Sobolev":[160],"Error":[161],"baseline,":[162],"5x":[164],"fewer":[165],"hypernetwork-based":[169],"alternative.":[170]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-12T00:00:00"}
