{"id":"https://openalex.org/W4414688583","doi":"https://doi.org/10.48550/arxiv.2507.08906","title":"Physics-informed machine learning: A mathematical framework with applications to time series forecasting","display_name":"Physics-informed machine learning: A mathematical framework with applications to time series forecasting","publication_year":2025,"publication_date":"2025-07-11","ids":{"openalex":"https://openalex.org/W4414688583","doi":"https://doi.org/10.48550/arxiv.2507.08906"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.08906","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.08906","pdf_url":"https://arxiv.org/pdf/2507.08906","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.08906","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060672047","display_name":"Nathan Doum\u00e8che","orcid":"https://orcid.org/0009-0005-4781-4006"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Doum\u00e8che, Nathan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060672047"],"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/T11052","display_name":"Energy Load and Power Forecasting","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11052","display_name":"Energy Load and Power Forecasting","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T12676","display_name":"Machine Learning and ELM","score":0.9861000180244446,"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/T10320","display_name":"Neural Networks and Applications","score":0.9527000188827515,"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/kernel","display_name":"Kernel (algebra)","score":0.5692999958992004},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4821000099182129},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.4652000069618225},{"id":"https://openalex.org/keywords/energy-consumption","display_name":"Energy consumption","score":0.4404999911785126},{"id":"https://openalex.org/keywords/electricity","display_name":"Electricity","score":0.38370001316070557},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.3659999966621399},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.36559998989105225},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.3619999885559082},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.34310001134872437}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6836000084877014},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5692999958992004},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.49140000343322754},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4684000015258789},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C206658404","wikidata":"https://www.wikidata.org/wiki/Q12725","display_name":"Electricity","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.36559998989105225},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C2982736386","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Statistical learning","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C77715397","wikidata":"https://www.wikidata.org/wiki/Q931447","display_name":"Electrical load","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C193809577","wikidata":"https://www.wikidata.org/wiki/Q3409300","display_name":"Demand forecasting","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C13736549","wikidata":"https://www.wikidata.org/wiki/Q4489420","display_name":"Industrial engineering","level":1,"score":0.3027999997138977},{"id":"https://openalex.org/C161657586","wikidata":"https://www.wikidata.org/wiki/Q1203326","display_name":"Technology forecasting","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C122282355","wikidata":"https://www.wikidata.org/wiki/Q7246855","display_name":"Probabilistic forecasting","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C115903097","wikidata":"https://www.wikidata.org/wiki/Q7094097","display_name":"Online machine learning","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C30772137","wikidata":"https://www.wikidata.org/wiki/Q5164762","display_name":"Consumption (sociology)","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C2779915298","wikidata":"https://www.wikidata.org/wiki/Q7604400","display_name":"Statistical learning theory","level":3,"score":0.274399995803833},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26759999990463257},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2574000060558319},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.08906","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.08906","pdf_url":"https://arxiv.org/pdf/2507.08906","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2507.08906","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.08906","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.08906","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.08906","pdf_url":"https://arxiv.org/pdf/2507.08906","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physics-informed":[0],"machine":[1,13],"learning":[2,14],"(PIML)":[3],"is":[4],"an":[5],"emerging":[6],"framework":[7,156],"that":[8,30],"integrates":[9],"physical":[10,17],"knowledge":[11],"into":[12],"models.":[15],"This":[16],"prior":[18],"often":[19],"takes":[20],"the":[21,31,37,45,55,87,133,144],"form":[22],"of":[23,40,48,57,64,89,146],"a":[24,154],"partial":[25],"differential":[26],"equation":[27],"(PDE)":[28],"system":[29],"regression":[32,92],"function":[33],"must":[34],"satisfy.":[35],"In":[36,51,98],"first":[38],"part":[39,118],"this":[41,102],"dissertation,":[42],"we":[43,53,100,152],"analyze":[44],"statistical":[46],"properties":[47,56],"PIML":[49,74],"methods.":[50],"particular,":[52],"study":[54],"physics-informed":[58,108],"neural":[59],"networks":[60],"(PINNs)":[61],"in":[62,122,162,173],"terms":[63],"approximation,":[65],"consistency,":[66],"overfitting,":[67],"and":[68,110,142,159,170],"convergence.":[69],"We":[70,129],"then":[71],"show":[72],"how":[73],"problems":[75],"can":[76],"be":[77],"framed":[78],"as":[79],"kernel":[80,90,103],"methods,":[81],"making":[82],"it":[83,166],"possible":[84],"to":[85,93,105,167],"apply":[86],"tools":[88],"ridge":[91],"better":[94],"understand":[95],"their":[96],"behavior.":[97],"addition,":[99],"use":[101],"formulation":[104],"develop":[106],"novel":[107],"algorithms":[109],"implement":[111],"them":[112],"efficiently":[113],"on":[114,137,148],"GPUs.":[115],"The":[116],"second":[117],"explores":[119],"industrial":[120],"applications":[121],"forecasting":[123,169,172],"energy":[124],"signals":[125],"during":[126],"atypical":[127],"periods.":[128],"present":[130],"results":[131],"from":[132],"Smarter":[134],"Mobility":[135],"challenge":[136],"electric":[138],"vehicle":[139],"charging":[140],"occupancy":[141],"examine":[143],"impact":[145],"mobility":[147],"electricity":[149],"demand.":[150],"Finally,":[151],"introduce":[153],"physics-constrained":[155],"for":[157],"designing":[158],"enforcing":[160],"constraints":[161],"time":[163],"series,":[164],"applying":[165],"load":[168],"tourism":[171],"various":[174],"countries.":[175]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}