{"id":"https://openalex.org/W7167043141","doi":"https://doi.org/10.48550/arxiv.2607.00364","title":"WarpagePINN: Thermal Warpage Prediction in Advanced Packaging via a Two-Stage Physics-Informed Neural Networks","display_name":"WarpagePINN: Thermal Warpage Prediction in Advanced Packaging via a Two-Stage Physics-Informed Neural Networks","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167043141","doi":"https://doi.org/10.48550/arxiv.2607.00364"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00364","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.00364","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139931608","display_name":"Xinyu Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Xinyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139889937","display_name":"Min Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Min","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103779396","display_name":"Z X Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Zeyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139860279","display_name":"Wenxing Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Wenxing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139873459","display_name":"Jianhua Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jianhua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139937894","display_name":"Liang Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Liang","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/T11527","display_name":"3D IC and TSV technologies","score":0.47119998931884766,"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/T11527","display_name":"3D IC and TSV technologies","score":0.47119998931884766,"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/T10460","display_name":"Electronic Packaging and Soldering Technologies","score":0.30559998750686646,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.03269999846816063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7024000287055969},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6148999929428101},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5889999866485596},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5446000099182129},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.5223000049591064},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.48910000920295715},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46720001101493835},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4490000009536743},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4471000134944916}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7024000287055969},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5889999866485596},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5446000099182129},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.5223000049591064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5141000151634216},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46720001101493835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4584999978542328},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.444599986076355},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C179717631","wikidata":"https://www.wikidata.org/wiki/Q2991667","display_name":"Multilayer perceptron","level":3,"score":0.4124000072479248},{"id":"https://openalex.org/C47463417","wikidata":"https://www.wikidata.org/wiki/Q6583695","display_name":"Thermal expansion","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C37292000","wikidata":"https://www.wikidata.org/wiki/Q1257918","display_name":"Residual stress","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.32519999146461487},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.2973000109195709},{"id":"https://openalex.org/C72293138","wikidata":"https://www.wikidata.org/wiki/Q909741","display_name":"Temperature measurement","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.2556000053882599},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00364","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,"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":"doi:10.48550/arxiv.2607.00364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00364","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,"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"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6647034287452698,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Thermal":[0],"warpage":[1,61,124],"has":[2],"become":[3],"a":[4,27,48,89,105,117,127,172,182],"critical":[5],"issue":[6],"in":[7,15,42,188],"advanced":[8],"packaging,":[9],"primarily":[10],"caused":[11],"by":[12,76],"the":[13,43,80,83,99,110,114,134,153,159],"mismatch":[14],"coefficients":[16],"of":[17,30,63,139,177,184],"thermal":[18],"expansion":[19],"(CTE)":[20],"among":[21],"heterogeneously":[22],"integrated":[23],"materials.":[24],"However,":[25],"only":[26],"limited":[28],"number":[29],"studies":[31],"have":[32],"focused":[33],"on":[34,72],"developing":[35],"computational":[36],"methods":[37],"for":[38,123],"coupled":[39],"thermal-warpage":[40],"prediction":[41],"chiplet.":[44],"This":[45],"paper":[46],"proposes":[47],"two-stage":[49],"physics-informed":[50],"neural":[51,66],"network":[52,100],"(WarpagePINN)":[53],"framework":[54,162],"to":[55,132,148],"compute":[56],"both":[57],"temperature":[58,84],"profile":[59],"and":[60,98],"deformation":[62],"chiplets.":[64],"The":[65],"networks":[67],"are":[68],"trained":[69,102],"without":[70],"relying":[71],"labeled":[73],"datasets":[74],"generated":[75],"conventional":[77,167],"simulators.":[78],"In":[79,113],"first":[81],"stage,":[82,116],"field":[85],"is":[86,101,121,145],"modeled":[87],"using":[88],"Fourier":[90],"series":[91],"representation":[92],"that":[93,158],"inherently":[94],"satisfies":[95],"boundary":[96],"conditions,":[97],"solely":[103],"through":[104],"loss":[106,136],"function":[107,137],"derived":[108],"from":[109],"governing":[111],"equation.":[112],"second":[115],"multilayer":[118],"perceptron":[119],"(MLP)":[120],"employed":[122],"prediction,":[125],"utilizing":[126],"novel":[128],"hybrid":[129],"supervisory":[130],"strategy":[131],"optimize":[133],"energy-based":[135],"instead":[138],"residual":[140],"loss.":[141],"A":[142],"parametric":[143],"WarpagePINN":[144,161],"also":[146],"developed":[147],"quantify":[149],"uncertainties":[150],"associated":[151],"with":[152,166,171],"CTE.":[154],"Numerical":[155],"results":[156],"show":[157],"proposed":[160],"achieves":[163],"excellent":[164],"agreement":[165],"finite":[168],"element":[169],"methods,":[170],"mean":[173],"absolute":[174],"error":[175],"(MAE)":[176],"0.2":[178],"\u03bcm,":[179],"while":[180],"achieving":[181],"speedup":[183],"approximately":[185],"1000":[186],"{\\times}":[187],"CTE":[189],"parameterization":[190],"studies.":[191]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}
