{"id":"https://openalex.org/W4417536790","doi":"https://doi.org/10.48550/arxiv.2506.15687","title":"S$^2$GPT-PINNs: Sparse and Small models for PDEs","display_name":"S$^2$GPT-PINNs: Sparse and Small models for PDEs","publication_year":2025,"publication_date":"2025-05-25","ids":{"openalex":"https://openalex.org/W4417536790","doi":"https://doi.org/10.48550/arxiv.2506.15687"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.15687","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.15687","pdf_url":"https://arxiv.org/pdf/2506.15687","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.15687","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ji, Yajie","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ji, Yajie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Chen, Yanlai","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yanlai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Koohy, Shawn","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koohy, Shawn","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":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/T11948","display_name":"Machine Learning in Materials Science","score":0.0,"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/sparse-neural-networks","display_name":"sparse neural networks","score":0.6819999814033508},{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.8730000257492065},{"id":"https://openalex.org/keywords/parametric-partial-differential-equations","display_name":"parametric partial differential equations","score":0.9769999980926514},{"id":"https://openalex.org/keywords/knowledge-distillation","display_name":"knowledge distillation","score":0.8619999885559082},{"id":"https://openalex.org/keywords/physics-informed-loss-function","display_name":"physics-informed loss function","score":0.777999997138977},{"id":"https://openalex.org/keywords/small-language-models","display_name":"small language models","score":0.5720000267028809},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"greedy algorithm","score":0.527999997138977},{"id":"https://openalex.org/keywords/model-compression","display_name":"model compression","score":0.531000018119812}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5873000025749207},{"id":"https://openalex.org/C2779280203","wikidata":"https://www.wikidata.org/wiki/Q17121211","display_name":"Small data","level":2,"score":0.5636000037193298},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5555999875068665},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4830000102519989},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4424000084400177},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3617999851703644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3544999957084656},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C204030448","wikidata":"https://www.wikidata.org/wiki/Q101017","display_name":"Distillation","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29179999232292175},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C126691448","wikidata":"https://www.wikidata.org/wiki/Q2028919","display_name":"Magnitude (astronomy)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.26109999418258667}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.15687","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.15687","pdf_url":"https://arxiv.org/pdf/2506.15687","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.2506.15687","doi":"https://doi.org/10.48550/arxiv.2506.15687","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.15687","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.15687","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.15687","pdf_url":"https://arxiv.org/pdf/2506.15687","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"S$^2$GPT-PINN,":[2],"a":[3,40,49,100],"sparse":[4],"and":[5,29,35],"small":[6,41,126],"model":[7],"for":[8],"solving":[9],"parametric":[10],"partial":[11],"differential":[12],"equations":[13],"(PDEs).":[14],"Similar":[15],"to":[16,24,72,121],"Small":[17],"Language":[18],"Models":[19],"(SLMs),":[20],"S$^2$GPT-PINN":[21,62],"is":[22,55,84,99],"tailored":[23],"domain-specific":[25],"(families":[26],"of)":[27],"PDEs":[28],"characterized":[30],"by":[31,57,117],"its":[32],"compact":[33],"architecture":[34],"minimal":[36],"computational":[37],"power.":[38],"Leveraging":[39],"amount":[42],"of":[43,66,80,108,114,119,124],"extremely":[44,74],"high":[45,75],"quality":[46],"data":[47,115],"via":[48,77,87],"mathematically":[50],"rigorous":[51],"greedy":[52],"algorithm":[53],"that":[54,91],"enabled":[56],"the":[58,105,109,112,122,125],"large":[59],"full-order":[60],"models,":[61],"relies":[63],"on":[64],"orders":[65,118],"magnitude":[67,120],"less":[68],"parameters":[69],"than":[70],"PINNs":[71],"achieve":[73],"efficiency":[76],"two":[78],"levels":[79],"customizations.":[81],"The":[82,97],"first":[83],"knowledge":[85],"distillation":[86],"task-specific":[88],"activation":[89],"functions":[90],"are":[92],"transferred":[93],"from":[94],"Pre-Trained":[95],"PINNs.":[96],"second":[98],"judicious":[101],"down-sampling":[102],"when":[103],"calculating":[104],"physics-informed":[106],"loss":[107],"network":[110],"compressing":[111],"number":[113],"sites":[116],"size":[123],"model.":[127]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
