{"id":"https://openalex.org/W7133334109","doi":"https://doi.org/10.1007/s10444-026-10294-8","title":"Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations","display_name":"Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations","publication_year":2026,"publication_date":"2026-03-03","ids":{"openalex":"https://openalex.org/W7133334109","doi":"https://doi.org/10.1007/s10444-026-10294-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10294-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10294-8","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127944599","display_name":"Harsh Sharma","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harsh Sharma","raw_affiliation_strings":["Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, USA"],"raw_orcid":"https://orcid.org/0000-0001-8411-2285","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089927791","display_name":"Juan Diego Draxl Giannoni","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan Diego Draxl Giannoni","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123601657","display_name":"Boris Kr\u00e4mer","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris Kramer","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5127944599"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":6.9902,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.94953364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"52","issue":"2","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":0.9894999861717224,"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":0.9894999861717224,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.005499999970197678,"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/T11416","display_name":"Numerical methods for differential equations","score":0.0010000000474974513,"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/lift","display_name":"Lift (data mining)","score":0.7304999828338623},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6985999941825867},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6208999752998352},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5950999855995178},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4645000100135803},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.46230000257492065},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.3734999895095825},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.33009999990463257}],"concepts":[{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.7304999828338623},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6985999941825867},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6208999752998352},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5950999855995178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.590499997138977},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4772999882698059},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4645000100135803},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.46230000257492065},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3930000066757202},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3472999930381775},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.2964000105857849},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26489999890327454},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2533000111579895},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-026-10294-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10294-8","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G495503751","display_name":"CAREER: Goal-Oriented Variable Transformations for Efficient Reduced-Order and Data-Driven Modeling","funder_award_id":"2144023","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7193676759","display_name":null,"funder_award_id":"N000142212624","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1665592869","https://openalex.org/W1967577607","https://openalex.org/W1993134778","https://openalex.org/W2002308788","https://openalex.org/W2024908520","https://openalex.org/W2061788616","https://openalex.org/W2091254711","https://openalex.org/W2127135659","https://openalex.org/W2297679915","https://openalex.org/W2332297685","https://openalex.org/W2515869736","https://openalex.org/W2530996620","https://openalex.org/W2950169853","https://openalex.org/W2963008012","https://openalex.org/W2964868716","https://openalex.org/W2998362785","https://openalex.org/W3008005432","https://openalex.org/W3013279290","https://openalex.org/W3025789774","https://openalex.org/W3099887646","https://openalex.org/W3128115457","https://openalex.org/W3204767667","https://openalex.org/W4200357168","https://openalex.org/W4288092721","https://openalex.org/W4328051924","https://openalex.org/W4366444733","https://openalex.org/W4385208348","https://openalex.org/W4385437902","https://openalex.org/W4385678867","https://openalex.org/W4386119450","https://openalex.org/W4386236687","https://openalex.org/W4386534940","https://openalex.org/W4388162976","https://openalex.org/W4389453886","https://openalex.org/W4390025446","https://openalex.org/W4392265468","https://openalex.org/W4392815863","https://openalex.org/W4400841014","https://openalex.org/W4403927062","https://openalex.org/W4407145385","https://openalex.org/W4414555605"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-03-04T00:00:00"}