{"id":"https://openalex.org/W7150956331","doi":"https://doi.org/10.48550/arxiv.2604.02601","title":"WGFINNs: Weak formulation-based GENERIC formalism informed neural networks","display_name":"WGFINNs: Weak formulation-based GENERIC formalism informed neural networks","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7150956331","doi":"https://doi.org/10.48550/arxiv.2604.02601"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02601","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.02601","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066077873","display_name":"Jun Sur Richard Park","orcid":"https://orcid.org/0000-0003-4384-6412"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, Jun Sur Richard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132922425","display_name":"Auroni  Huque Hashim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hashim, Auroni Huque","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122919650","display_name":"Siu Wun Cheung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheung, Siu Wun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133021649","display_name":"Youngsoo Choi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, Youngsoo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023632213","display_name":"Yeonjong Shin","orcid":"https://orcid.org/0000-0003-4577-1979"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shin, Yeonjong","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.9797000288963318,"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":0.9797000288963318,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.00430000014603138,"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"}},{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.004100000020116568,"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/formalism","display_name":"Formalism (music)","score":0.6367999911308289},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6148999929428101},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5794000029563904},{"id":"https://openalex.org/keywords/noisy-data","display_name":"Noisy data","score":0.5303999781608582},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.5295000076293945},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5230000019073486},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.30239999294281006}],"concepts":[{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6367999911308289},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6148999929428101},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5794000029563904},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.5295000076293945},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5230000019073486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4745999872684479},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3919999897480011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36390000581741333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3472000062465668},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30790001153945923},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2565000057220459},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02601","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":"doi:10.48550/arxiv.2604.02601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02601","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"Data-driven":[0],"discovery":[1],"of":[2,31,67,74,87,137,175],"governing":[3],"equations":[4],"from":[5],"noisy":[6,81,148],"observations":[7],"remains":[8],"a":[9,24,96,101],"fundamental":[10],"challenge":[11],"in":[12,134],"scientific":[13],"machine":[14],"learning.":[15],"While":[16],"GENERIC":[17,56,88],"formalism":[18,57],"informed":[19,58],"neural":[20,59],"networks":[21,60],"(GFINNs)":[22],"provide":[23],"principled":[25],"framework":[26],"that":[27,159],"enforces":[28],"the":[29,64,71,118,121,125,130,135,140],"laws":[30],"thermodynamics":[32],"by":[33],"construction,":[34],"their":[35],"reliance":[36],"on":[37],"strong-form":[38,119,126],"loss":[39,99],"formulations":[40],"makes":[41],"them":[42],"highly":[43],"sensitive":[44],"to":[45,80,105],"measurement":[46],"noise.":[47],"To":[48],"address":[49],"this":[50],"limitation,":[51],"we":[52],"propose":[53],"weak":[54,65],"formulation-based":[55],"(WGFINNs),":[61],"which":[62],"integrate":[63],"formulation":[66],"dynamical":[68],"systems":[69],"with":[70,147],"structure-preserving":[72],"architecture":[73],"GFINNs.":[75],"WGFINNs":[76,160],"significantly":[77],"enhance":[78],"robustness":[79],"data":[82,149],"while":[83,139],"retaining":[84],"exact":[85],"satisfaction":[86],"degeneracy":[89],"and":[90,100,120,172],"symmetry":[91],"conditions.":[92,155],"We":[93],"further":[94],"incorporate":[95],"state-wise":[97],"weighted":[98],"residual-based":[102],"attention":[103],"mechanism":[104],"mitigate":[106],"scale":[107],"imbalance":[108],"across":[109],"state":[110],"variables.":[111],"Theoretical":[112],"analysis":[113],"contrasts":[114],"quantitative":[115],"differences":[116],"between":[117],"weak-form":[122,141],"estimators.":[123],"Mainly,":[124],"estimator":[127,142],"diverges":[128],"as":[129],"time":[131],"step":[132],"decreases":[133],"presence":[136],"noise,":[138],"can":[143],"be":[144],"accurate":[145,170],"even":[146],"if":[150],"test":[151],"functions":[152],"satisfy":[153],"certain":[154],"Numerical":[156],"experiments":[157],"demonstrate":[158],"consistently":[161],"outperform":[162],"GFINNs":[163],"at":[164],"varying":[165],"noise":[166],"levels,":[167],"achieving":[168],"more":[169],"predictions":[171],"reliable":[173],"recovery":[174],"physical":[176],"quantities.":[177]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-07T00:00:00"}
