{"id":"https://openalex.org/W7172420751","doi":"https://doi.org/10.48550/arxiv.2608.00516","title":"Machine-Learning-Compatible CALPHAD-type Optimization from Phase Equilibria by Auto-differentiation","display_name":"Machine-Learning-Compatible CALPHAD-type Optimization from Phase Equilibria by Auto-differentiation","publication_year":2026,"publication_date":"2026-08-01","ids":{"openalex":"https://openalex.org/W7172420751","doi":"https://doi.org/10.48550/arxiv.2608.00516"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.00516","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.00516","pdf_url":"https://arxiv.org/pdf/2608.00516","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/2608.00516","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052154284","display_name":"Wenhao Zhang","orcid":"https://orcid.org/0000-0003-3359-1882","observed_orcids":["https://orcid.org/0000-0003-3359-1882"]},"institutions":[{"id":"https://openalex.org/I205401836","display_name":"National Institute for Materials Science","ror":"https://ror.org/026v1ze26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205401836"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Zhang, Wenhao","raw_affiliation_strings":["International Center for Young Scientists (ICYS) , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Center for Young Scientists (ICYS) , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan","institution_ids":["https://openalex.org/I205401836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086262542","display_name":"Jean\u2010Claude Crivello","orcid":"https://orcid.org/0000-0002-4849-2556","observed_orcids":["https://orcid.org/0000-0002-4849-2556"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I205401836","display_name":"National Institute for Materials Science","ror":"https://ror.org/026v1ze26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205401836"]},{"id":"https://openalex.org/I4387153008","display_name":"LINK - Laboratory for Innovative Key Materials and Structures","ror":"https://ror.org/03qt6f440","country_code":"JP","type":"facility","lineage":["https://openalex.org/I123791789","https://openalex.org/I1294671590","https://openalex.org/I205401836","https://openalex.org/I4387153008"]}],"countries":["FR","JP"],"is_corresponding":false,"raw_author_name":"Crivello, Jean-Claude","raw_affiliation_strings":["CNRS-Saint-Gobain-NIMS , IRL 3629 , Laboratory for Innovative Key Materials and Structures (LINK) , 1-1 Namiki , Tsukuba , 305-0044 , Ibaraki , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS-Saint-Gobain-NIMS , IRL 3629 , Laboratory for Innovative Key Materials and Structures (LINK) , 1-1 Namiki , Tsukuba , 305-0044 , Ibaraki , Japan","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I205401836","https://openalex.org/I4387153008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025670532","display_name":"Yusuke Matsuoka","orcid":"https://orcid.org/0000-0001-5300-1726","observed_orcids":["https://orcid.org/0000-0001-5300-1726"]},"institutions":[{"id":"https://openalex.org/I205401836","display_name":"National Institute for Materials Science","ror":"https://ror.org/026v1ze26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205401836"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Matsuoka, Yusuke","raw_affiliation_strings":["Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan","institution_ids":["https://openalex.org/I205401836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035021303","display_name":"Toshiyuki Koyama","orcid":"https://orcid.org/0000-0001-7424-4858","observed_orcids":["https://orcid.org/0000-0001-7424-4858"]},"institutions":[{"id":"https://openalex.org/I205401836","display_name":"National Institute for Materials Science","ror":"https://ror.org/026v1ze26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205401836"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Koyama, Toshiyuki","raw_affiliation_strings":["Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan","institution_ids":["https://openalex.org/I205401836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027537776","display_name":"Taichi Abe","orcid":"https://orcid.org/0000-0002-5065-0939","observed_orcids":["https://orcid.org/0000-0002-5065-0939"]},"institutions":[{"id":"https://openalex.org/I205401836","display_name":"National Institute for Materials Science","ror":"https://ror.org/026v1ze26","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205401836"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Abe, Taichi","raw_affiliation_strings":["Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center for Structure Materials , National Institute for Materials Science (NIMS) , Sengen 1-2-1 , Tsukuba , Ibaraki 305-0047 , Japan","institution_ids":["https://openalex.org/I205401836"]}]}],"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":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/T11948","display_name":"Machine Learning in Materials Science","score":0.9365000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9365000128746033,"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"}},{"id":"https://openalex.org/T11126","display_name":"Metallurgical Processes and Thermodynamics","score":0.04439999908208847,"subfield":{"id":"https://openalex.org/subfields/2506","display_name":"Metals and Alloys"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13645","display_name":"Thermodynamic and Structural Properties of Metals and Alloys","score":0.01209999993443489,"subfield":{"id":"https://openalex.org/subfields/2506","display_name":"Metals and Alloys"},"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/calphad","display_name":"CALPHAD","score":0.8709999918937683},{"id":"https://openalex.org/keywords/phase-equilibria","display_name":"phase equilibria","score":0.8989999890327454},{"id":"https://openalex.org/keywords/differentiable-loss-function","display_name":"differentiable loss function","score":0.8379999995231628},{"id":"https://openalex.org/keywords/auto-differentiation","display_name":"auto-differentiation","score":0.9769999980926514},{"id":"https://openalex.org/keywords/phase-boundaries","display_name":"phase boundaries","score":0.7089999914169312},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.921999990940094},{"id":"https://openalex.org/keywords/ternary-systems","display_name":"ternary systems","score":0.7609999775886536},{"id":"https://openalex.org/keywords/pytorch","display_name":"PyTorch","score":0.7440000176429749}],"concepts":[{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5424000024795532},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5394999980926514},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.5059999823570251},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48890000581741333},{"id":"https://openalex.org/C105236789","wikidata":"https://www.wikidata.org/wiki/Q213016","display_name":"Thermodynamic process","level":3,"score":0.43619999289512634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4212000072002411},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.4165000021457672},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.388700008392334},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.37860000133514404},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3544999957084656},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3271999955177307},{"id":"https://openalex.org/C2778049539","wikidata":"https://www.wikidata.org/wiki/Q17002908","display_name":"Bayesian optimization","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C12668873","wikidata":"https://www.wikidata.org/wiki/Q230875","display_name":"Thermodynamic state","level":3,"score":0.3203999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.303600013256073},{"id":"https://openalex.org/C141780669","wikidata":"https://www.wikidata.org/wiki/Q7783161","display_name":"Thermodynamic integration","level":3,"score":0.29120001196861267},{"id":"https://openalex.org/C41607394","wikidata":"https://www.wikidata.org/wiki/Q2420179","display_name":"Thermodynamic potential","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C31555180","wikidata":"https://www.wikidata.org/wiki/Q3523867","display_name":"Material properties","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C2986159531","wikidata":"https://www.wikidata.org/wiki/Q752412","display_name":"Phase equilibrium","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.00516","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.00516","pdf_url":"https://arxiv.org/pdf/2608.00516","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.2608.00516","doi":"https://doi.org/10.48550/arxiv.2608.00516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.00516","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:2608.00516","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.00516","pdf_url":"https://arxiv.org/pdf/2608.00516","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7172420751.pdf","grobid_xml":"https://content.openalex.org/works/W7172420751.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4407759102"],"related_works":["https://openalex.org/W4416697866","https://openalex.org/W7202382030","https://openalex.org/W4413680437","https://openalex.org/W3129512930","https://openalex.org/W7135208444","https://openalex.org/W7116778864","https://openalex.org/W2565263391","https://openalex.org/W4392954229","https://openalex.org/W7125483518","https://openalex.org/W4399460431"],"abstract_inverted_index":{"To":[0],"accurately":[1],"determine":[2],"phase":[3,6,12,24,166],"boundaries":[4],"and":[5,72,114],"transitions,":[7],"thermodynamic":[8,31,65,88,101,140,150],"models":[9,102,151],"that":[10,39,67],"describe":[11],"free":[13],"energies":[14],"often":[15,35],"have":[16],"to":[17,96,146],"be":[18,69,92,144],"optimized":[19,93],"based":[20,63],"on":[21,64],"experimentally":[22],"observed":[23],"equilibria.":[25,167],"While":[26],"different":[27,118],"approaches":[28],"exist":[29],"for":[30],"optimization,":[32],"they":[33],"are":[34,40],"implemented":[36],"in":[37,78,103,117,152],"ways":[38],"not":[41],"compatible":[42],"with":[43,94,123],"machine":[44,148],"learning":[45,149],"workflows":[46],"requiring":[47],"differentiable":[48],"calculation":[49],"of":[50,106,135,138,160],"the":[51,79,104,129,136,139],"loss":[52,61,85,130],"function.":[53],"In":[54,154],"this":[55,84],"work,":[56],"we":[57,111,156],"derive":[58],"a":[59],"phase-equilibrium":[60],"function":[62,131],"potentials":[66],"can":[68,91,143],"efficiently":[70],"evaluated":[71],"enables":[73],"gradient-based":[74],"optimization":[75,116,159],"by":[76],"auto-differentiation":[77],"\\texttt{PyTorch}":[80],"package.":[81],"By":[82],"minimizing":[83],"function,":[86],"general":[87],"model":[89],"parameters":[90],"respect":[95],"experimental":[97],"phase-equilibria":[98],"data.":[99],"Using":[100],"CALculation":[105],"PHAse":[107],"Diagram":[108],"(CALPHAD)":[109],"framework,":[110],"illustrate":[112],"successful":[113],"efficient":[115],"systems,":[119],"including":[120],"ternary":[121],"systems":[122],"more":[124],"than":[125],"100":[126],"parameters.":[127],"As":[128],"is":[132],"defined":[133],"independently":[134],"details":[137],"models,":[141],"it":[142],"used":[145],"optimize":[147],"general.":[153],"particular,":[155],"demonstrate":[157],"top-down":[158],"an":[161],"atomistic":[162],"potential":[163],"from":[164],"target":[165]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-05T00:00:00"}