{"id":"https://openalex.org/W4415316580","doi":"https://doi.org/10.48550/arxiv.2510.06684","title":"AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networks","display_name":"AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networks","publication_year":2025,"publication_date":"2025-10-08","ids":{"openalex":"https://openalex.org/W4415316580","doi":"https://doi.org/10.48550/arxiv.2510.06684"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.06684","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.06684","pdf_url":"https://arxiv.org/pdf/2510.06684","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","license_id":"https://openalex.org/licenses/cc-by","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/2510.06684","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100603585","display_name":"Kang An","orcid":"https://orcid.org/0000-0003-3635-3070","observed_orcids":["https://orcid.org/0000-0003-3635-3070"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"An, Kang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055897166","display_name":"Chenhao Si","orcid":"https://orcid.org/0009-0006-5314-4632","observed_orcids":["https://orcid.org/0009-0006-5314-4632"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Si, Chenhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Yan, Ming","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008787209","display_name":"Shiqian Ma","orcid":"https://orcid.org/0000-0003-1967-1069","observed_orcids":["https://orcid.org/0000-0003-1967-1069"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Shiqian","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":2,"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":1.0,"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":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.0,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":1.0},{"id":"https://openalex.org/keywords/adaptive-optimizers","display_name":"adaptive optimization algorithm","score":0.7760000228881836},{"id":"https://openalex.org/keywords/preconditioning","display_name":"preconditioning","score":0.628000020980835},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.8740000128746033}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6913999915122986},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6585999727249146},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6517000198364258},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.602400004863739},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.49149999022483826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4442000091075897},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4381999969482422},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39160001277923584},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.32739999890327454},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.31150001287460327},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.26600000262260437},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.06684","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.06684","pdf_url":"https://arxiv.org/pdf/2510.06684","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.06684","doi":"https://doi.org/10.48550/arxiv.2510.06684","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.06684","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.06684","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.06684","pdf_url":"https://arxiv.org/pdf/2510.06684","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4414359866","https://openalex.org/W4408489371","https://openalex.org/W7210289476","https://openalex.org/W7166093851","https://openalex.org/W4395075104","https://openalex.org/W4229015109","https://openalex.org/W4362736676","https://openalex.org/W4409581239","https://openalex.org/W4414509513","https://openalex.org/W7131304719"],"abstract_inverted_index":{"Physics-Informed":[0],"Neural":[1],"Networks":[2],"(PINNs)":[3],"provide":[4],"a":[5,77,98],"powerful":[6],"and":[7,42,50,113,145,153],"general":[8],"framework":[9],"for":[10],"solving":[11],"Partial":[12],"Differential":[13],"Equations":[14],"(PDEs)":[15],"by":[16,59,141],"embedding":[17],"physical":[18],"laws":[19],"into":[20],"loss":[21,36,86,111],"functions.":[22],"However,":[23],"training":[24,101],"PINNs":[25],"is":[26,72,150],"notoriously":[27],"difficult":[28],"due":[29],"to":[30,33,80,109,152],"the":[31,115,143],"need":[32],"balance":[34],"multiple":[35],"terms,":[37],"such":[38],"as":[39,75,139],"PDE":[40,124],"residuals":[41],"boundary":[43],"conditions,":[44],"which":[45],"often":[46],"have":[47],"conflicting":[48],"objectives":[49],"vastly":[51],"different":[52],"curvatures.":[53],"Existing":[54],"methods":[55],"address":[56],"this":[57,70,93],"issue":[58],"manipulating":[60],"gradients":[61,82],"before":[62],"optimization":[63],"(a":[64],"\"pre-combine\"":[65],"strategy).":[66],"We":[67],"argue":[68],"that":[69,127],"approach":[71],"fundamentally":[73],"limited,":[74],"forcing":[76],"single":[78],"optimizer":[79,108],"process":[81],"from":[83],"spectrally":[84],"heterogeneous":[85],"landscapes":[87],"disrupts":[88],"its":[89],"internal":[90],"preconditioning.":[91],"In":[92],"work,":[94],"we":[95],"introduce":[96],"AutoBalance,":[97],"novel":[99],"\"post-combine\"":[100],"paradigm.":[102],"AutoBalance":[103,128,149],"assigns":[104],"an":[105],"independent":[106],"adaptive":[107],"each":[110],"component":[112],"aggregates":[114],"resulting":[116],"preconditioned":[117],"updates":[118],"afterwards.":[119],"Extensive":[120],"experiments":[121],"on":[122,163],"challenging":[123],"benchmarks":[125],"show":[126],"consistently":[129],"outperforms":[130],"existing":[131],"frameworks,":[132],"achieving":[133],"significant":[134],"reductions":[135],"in":[136],"solution":[137],"error,":[138],"measured":[140],"both":[142],"MSE":[144],"$L^{\\infty}$":[146],"norms.":[147],"Moreover,":[148],"orthogonal":[151],"complementary":[154],"with":[155],"other":[156],"popular":[157],"PINN":[158],"methodologies,":[159],"amplifying":[160],"their":[161],"effectiveness":[162],"demanding":[164],"benchmarks.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-18T00:00:00"}