{"id":"https://openalex.org/W7204098669","doi":"https://doi.org/10.48550/arxiv.2608.20404","title":"Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model","display_name":"Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model","publication_year":2026,"publication_date":"2026-08-04","ids":{"openalex":"https://openalex.org/W7204098669","doi":"https://doi.org/10.48550/arxiv.2608.20404"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20404","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20404","pdf_url":"https://arxiv.org/pdf/2608.20404","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.20404","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102778145","display_name":"Partha Sarathi Mondal","orcid":"https://orcid.org/0009-0009-1414-288X","observed_orcids":["https://orcid.org/0009-0009-1414-288X"]},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mondal, Partha Sarathi","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005","institution_ids":["https://openalex.org/I56404289"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148030823","display_name":"Manav Kumar Jalan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jalan, Manav Kumar","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005","institution_ids":["https://openalex.org/I56404289"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147986915","display_name":"Anish Kumar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kumar, Anish","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005","institution_ids":["https://openalex.org/I56404289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133309557","display_name":"Shradha Mishra","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mishra, Shradha","raw_affiliation_strings":["Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Indian Institute of Technology (BHU) Varanasi , India 221005","institution_ids":["https://openalex.org/I56404289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I56404289"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9984999895095825,"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":0.9984999895095825,"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/T11236","display_name":"Control Systems and Identification","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":9.999999747378752e-05,"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/phase-ordering-kinetics","display_name":"phase ordering kinetics","score":0.9739999771118164},{"id":"https://openalex.org/keywords/allen-cahn-equation","display_name":"Allen-Cahn equation","score":0.9919999837875366},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.9700000286102295},{"id":"https://openalex.org/keywords/stability-selection","display_name":"stability selection","score":0.8980000019073486},{"id":"https://openalex.org/keywords/noise-sensitivity","display_name":"noise sensitivity","score":0.6570000052452087},{"id":"https://openalex.org/keywords/coefficient-recovery","display_name":"coefficient recovery","score":0.7590000033378601},{"id":"https://openalex.org/keywords/phase-separation","display_name":"phase separation","score":0.7519999742507935},{"id":"https://openalex.org/keywords/coarsening","display_name":"coarsening","score":0.8759999871253967},{"id":"https://openalex.org/keywords/coarse-grained-models","display_name":"coarse-grained models","score":0.6169999837875366},{"id":"https://openalex.org/keywords/spatio-temporal-data","display_name":"spatio-temporal data","score":0.9480000138282776}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.8626000285148621},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5828999876976013},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5074999928474426},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3758000135421753},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.33149999380111694},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2890999913215637},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.28700000047683716},{"id":"https://openalex.org/C128805008","wikidata":"https://www.wikidata.org/wiki/Q722878","display_name":"Master equation","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27630001306533813},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2635999917984009},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.25780001282691956}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20404","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20404","pdf_url":"https://arxiv.org/pdf/2608.20404","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.20404","doi":"https://doi.org/10.48550/arxiv.2608.20404","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20404","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.20404","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20404","pdf_url":"https://arxiv.org/pdf/2608.20404","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2392820929","display_name":null,"funder_award_id":"MTR/2021/000438","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G3536088198","display_name":null,"funder_award_id":"CRG/2021/006945","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G3759446790","display_name":null,"funder_award_id":"CRG/2021/006945","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G8867279608","display_name":null,"funder_award_id":"MTR/2021/000438","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320306227","display_name":"Arthritis National Research Foundation","ror":"https://ror.org/03abbex33"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204098669.pdf","grobid_xml":"https://content.openalex.org/works/W7204098669.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4368303491"],"related_works":["https://openalex.org/W3211465333","https://openalex.org/W7129049539","https://openalex.org/W4312010698","https://openalex.org/W2972630188","https://openalex.org/W7170078291","https://openalex.org/W4415957638","https://openalex.org/W4399120457","https://openalex.org/W4388706706","https://openalex.org/W7223129229","https://openalex.org/W4388282888"],"abstract_inverted_index":{"Data-driven":[0],"discovery":[1],"of":[2,16,25,55,59,68,135,157,168,177,186],"governing":[3,85],"equations":[4],"from":[5],"spatiotemporal":[6],"data":[7,56],"offers":[8],"a":[9,36,47],"promising":[10],"route":[11],"to":[12,102],"obtaining":[13],"coarse-grained":[14,148],"descriptions":[15],"complex":[17],"dynamical":[18],"systems.":[19],"Here,":[20],"we":[21],"investigate":[22],"the":[23,32,39,53,60,66,69,80,84,94,110,133,139,146,151,158,166,175,180,184],"performance":[24],"PDE-SINDy":[26,76,169],"for":[27,170],"discovering":[28],"phase-ordering":[29,171],"dynamics":[30,45,86,156],"using":[31],"Allen--Cahn":[33],"equation":[34,70,136,149,187],"as":[35,46],"benchmark":[37],"and":[38,63,119,131,154],"Ising":[40,143],"model":[41,144],"with":[42,125],"Glauber":[43,140],"spin-flip":[44],"microscopic":[48,160],"system.":[49,161],"We":[50,72,105],"systematically":[51],"analyze":[52],"effects":[54],"availability,":[57],"size":[58],"candidate":[61,111],"library,":[62],"noise":[64],"on":[65],"efficiency":[67,134,185],"discovery.":[71,137,188],"find":[73],"that":[74,108,182],"stability-selection":[75],"can":[77,113],"robustly":[78],"identify":[79],"relevant":[81],"terms":[82],"in":[83],"even":[87],"under":[88],"limited":[89],"or":[90],"noisy":[91],"data,":[92],"while":[93,173],"recovered":[95],"coefficient":[96,120],"values":[97],"are":[98],"substantially":[99],"more":[100],"sensitive":[101],"these":[103],"factors.":[104],"further":[106],"show":[107],"enlarging":[109],"library":[112,123],"strongly":[114],"affect":[115],"both":[116],"term":[117],"identification":[118],"recovery.":[121],"Incorporating":[122],"bagging":[124],"stability":[126],"selection":[127],"reduces":[128],"this":[129],"sensitivity":[130],"improves":[132],"For":[138],"spin":[141],"flip":[142],"dynamics,":[145],"resulting":[147],"reproduces":[150],"characteristic":[152],"phase-separation":[153],"coarsening":[155],"underlying":[159],"Overall,":[162],"our":[163],"results":[164],"demonstrate":[165],"potential":[167],"systems":[172],"highlighting":[174],"importance":[176],"carefully":[178],"assessing":[179],"factors":[181],"influence":[183]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-25T00:00:00"}