{"id":"https://openalex.org/W7220722178","doi":"https://doi.org/10.48550/arxiv.2610.03947","title":"Synthesizing Physics Formulae with Transformers","display_name":"Synthesizing Physics Formulae with Transformers","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220722178","doi":"https://doi.org/10.48550/arxiv.2610.03947"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03947","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03947","pdf_url":"https://arxiv.org/pdf/2610.03947","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":"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/2610.03947","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153484456","display_name":"Shuwei Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wang, Shuwei","raw_affiliation_strings":["Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076298832","display_name":"Vadim V. Bulitko","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bulitko, Vadim","raw_affiliation_strings":["Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157680700","display_name":"Michael Youngblood","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Youngblood, Michael","raw_affiliation_strings":["Filuta AI , 1606 Headway Circle , Austin , TX 78754 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Filuta AI , 1606 Headway Circle , Austin , TX 78754 , USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033389483","display_name":"Ramon Lawrence","orcid":"https://orcid.org/0000-0002-6779-4461","observed_orcids":["https://orcid.org/0000-0002-6779-4461"]},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lawrence, Ramon","raw_affiliation_strings":["Department of Computer Science, Data Science , University of British Columbia , 6200 University Blvd , Vancouver , BC Canada V6T 1Z4 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Data Science , University of British Columbia , 6200 University Blvd , Vancouver , BC Canada V6T 1Z4 , Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030505534","display_name":"William Yeoh","orcid":"https://orcid.org/0000-0002-2617-870X","observed_orcids":["https://orcid.org/0000-0002-2617-870X","https://orcid.org/0000-0002-2964-4518"]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yeoh, William","raw_affiliation_strings":["McKelvey School of Engineering , Washington University in St. Louis , 1 Brookings Drive , St. Louis , MO 63130-4899 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McKelvey School of Engineering , Washington University in St. Louis , 1 Brookings Drive , St. Louis , MO 63130-4899 , USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157731908","display_name":"Shinichi Nakagawa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nakagawa, Shinichi","raw_affiliation_strings":["Department of Biology , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biology , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157715980","display_name":"Matthew R. G. Brown","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brown, Matthew R. G.","raw_affiliation_strings":["Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157790130","display_name":"Yu Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wang, Yu","raw_affiliation_strings":["Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science , University of Alberta , 116 Street and 85 Avenue , Edmonton , AB , T6G 2R3 , Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.7896000146865845,"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"}},"topics":[{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.7896000146865845,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.08079999685287476,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.03060000017285347,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/symbolic-regression","display_name":"symbolic regression","score":0.9660000205039978},{"id":"https://openalex.org/keywords/transformer","display_name":"transformer models","score":0.7289999723434448},{"id":"https://openalex.org/keywords/extrapolation","display_name":"extrapolation","score":0.8320000171661377},{"id":"https://openalex.org/keywords/overfitting","display_name":"overfitting","score":0.9660000205039978},{"id":"https://openalex.org/keywords/noise-robustness","display_name":"noise robustness","score":0.796999990940094},{"id":"https://openalex.org/keywords/fine-tuning","display_name":"fine-tuning","score":0.6740000247955322}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.7634000182151794},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.7475000023841858},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4674000144004822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4115000069141388},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03947","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03947","pdf_url":"https://arxiv.org/pdf/2610.03947","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03947","doi":"https://doi.org/10.48550/arxiv.2610.03947","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03947","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:2610.03947","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03947","pdf_url":"https://arxiv.org/pdf/2610.03947","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319946","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27"},{"id":"https://openalex.org/F4320331257","display_name":"Alliance de recherche num\u00e9rique du Canada","ror":"https://ror.org/010r6td27"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220722178.pdf","grobid_xml":"https://content.openalex.org/works/W7220722178.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2899663614","https://openalex.org/W4286224767","https://openalex.org/W4368303491","https://openalex.org/W4416256133","https://openalex.org/W6929378384"],"related_works":["https://openalex.org/W4392567326","https://openalex.org/W4394709598","https://openalex.org/W4323050423","https://openalex.org/W3166835815","https://openalex.org/W7213930919","https://openalex.org/W4389501019","https://openalex.org/W7222212176","https://openalex.org/W7171495061","https://openalex.org/W7133193052","https://openalex.org/W3102263967"],"abstract_inverted_index":{"Finding":[0],"a":[1,6,18,92,130,144],"compact":[2],"formula":[3,131],"that":[4,64,96],"fits":[5],"set":[7,86],"of":[8,36,48,87,159],"input-output":[9],"pairs":[10],"and":[11,94,125,136],"predicts":[12],"outputs":[13],"on":[14,43,106],"unseen":[15,77],"inputs":[16],"is":[17],"fundamental":[19],"problem":[20],"in":[21,120,132],"science.":[22],"Symbolic":[23],"regression":[24],"automates":[25],"the":[26,34,66,85,97,104,114,121],"search":[27],"for":[28],"such":[29],"formulae:":[30],"search-based":[31],"methods":[32,142,148],"explore":[33],"space":[35],"possible":[37],"formulae":[38,47,63,88,99,116],"directly,":[39],"while":[40],"transformers":[41],"pre-trained":[42],"synthetic":[44],"data":[45,68,107],"produce":[46],"comparable":[49,145],"quality":[50],"substantially":[51,101],"faster.":[52],"Existing":[53],"transformers,":[54],"however,":[55],"are":[56],"prone":[57],"to":[58,74,90,118,156],"overfitting":[59],"---":[60],"they":[61],"find":[62],"fit":[65],"training":[67],"well":[69],"but":[70],"do":[71],"not":[72],"extrapolate":[73,100],"input":[75],"ranges":[76],"during":[78],"training.":[79],"We":[80],"address":[81],"this":[82],"by":[83],"shaping":[84],"used":[89],"train":[91],"transformer,":[93],"show":[95],"resulting":[98],"better.":[102],"Fine-tuning":[103],"transformer":[105,128],"with":[108],"noise-corrupted":[109],"target":[110],"values":[111],"further":[112],"makes":[113],"synthesized":[115],"robust":[117],"noise":[119],"observations.":[122],"On":[123],"SRBench":[124],"LLM-SRBench":[126],"our":[127,150],"synthesizes":[129],"about":[133],"ten":[134],"seconds":[135],"extrapolates":[137],"better":[138],"than":[139],"all":[140],"evaluated":[141],"at":[143],"budget.":[146],"Search-based":[147],"surpass":[149],"accuracy":[151],"only":[152],"when":[153],"given":[154],"one":[155],"three":[157],"orders":[158],"magnitude":[160],"more":[161],"time.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-07T00:00:00"}