{"id":"https://openalex.org/W4310557235","doi":"https://doi.org/10.48550/arxiv.2211.16610","title":"Deep Learning Discrete Calculus (DLDC): A Family of Discrete Numerical Methods by Universal Approximation for STEM Education to Frontier Research","display_name":"Deep Learning Discrete Calculus (DLDC): A Family of Discrete Numerical Methods by Universal Approximation for STEM Education to Frontier Research","publication_year":2022,"publication_date":"2022-11-29","ids":{"openalex":"https://openalex.org/W4310557235","doi":"https://doi.org/10.48550/arxiv.2211.16610"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2211.16610","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2211.16610","pdf_url":"https://arxiv.org/pdf/2211.16610","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2211.16610","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072343066","display_name":"Sourav Saha","orcid":"https://orcid.org/0000-0001-6610-4820"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Saha, Sourav","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101546286","display_name":"Chanwook Park","orcid":"https://orcid.org/0000-0002-1208-5465"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, Chanwook","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048757931","display_name":"Stefan Knapik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Knapik, Stefan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045039452","display_name":"Jiachen Guo","orcid":"https://orcid.org/0000-0003-2500-377X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Jiachen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074408615","display_name":"Owen Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Owen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014509470","display_name":"Wing Kam Liu","orcid":"https://orcid.org/0000-0001-7725-8438"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Wing Kam","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5072343066"],"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9926999807357788,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9926999807357788,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9818999767303467,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9707000255584717,"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/numerical-analysis","display_name":"Numerical analysis","score":0.574853777885437},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5731651782989502},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.48250293731689453},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46483397483825684},{"id":"https://openalex.org/keywords/numerical-differentiation","display_name":"Numerical differentiation","score":0.45103228092193604},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4220477044582367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41943639516830444},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4181884527206421},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.41593384742736816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39016833901405334},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3055451810359955},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16843628883361816},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13534283638000488}],"concepts":[{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.574853777885437},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5731651782989502},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.48250293731689453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46483397483825684},{"id":"https://openalex.org/C154181440","wikidata":"https://www.wikidata.org/wiki/Q1683292","display_name":"Numerical differentiation","level":2,"score":0.45103228092193604},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4220477044582367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41943639516830444},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4181884527206421},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.41593384742736816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39016833901405334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3055451810359955},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16843628883361816},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13534283638000488},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2211.16610","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2211.16610","pdf_url":"https://arxiv.org/pdf/2211.16610","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2211.16610","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2211.16610","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2211.16610","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2211.16610","pdf_url":"https://arxiv.org/pdf/2211.16610","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7599999904632568,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2004744038","https://openalex.org/W1989109250","https://openalex.org/W4388482258","https://openalex.org/W3202647903","https://openalex.org/W2053129613","https://openalex.org/W2962937865","https://openalex.org/W2046931757","https://openalex.org/W2945760162","https://openalex.org/W2014574026","https://openalex.org/W2052447623"],"abstract_inverted_index":{"The":[0,39,101,158],"article":[1,102],"proposes":[2,170],"formulating":[3],"and":[4,47,54,89,122,135,176,197],"codifying":[5],"a":[6,62,142],"set":[7],"of":[8,36,51,57,65,79,91,94,116,166,190],"applied":[9,37],"numerical":[10,25,58,66,92,129,192],"methods,":[11,193],"coined":[12],"as":[13,83,85,132],"Deep":[14],"Learning":[15],"Discrete":[16],"Calculus":[17],"(DLDC),":[18],"that":[19,68],"uses":[20],"the":[21,29,34,45,77,87,95,110,113,117,163,167,191],"knowledge":[22],"from":[23],"discrete":[24],"methods":[26,41,119,130,138],"to":[27,43,60,75,127,144,180],"interpret":[28],"deep":[30,52,123],"learning":[31,53,124],"algorithms":[32],"through":[33],"lens":[35],"mathematics.":[38],"DLDC":[40,118,195],"aim":[42],"leverage":[44],"flexibility":[46],"ever":[48],"increasing":[49],"resources":[50],"rich":[55],"literature":[56],"analysis":[59],"formulate":[61],"general":[63],"class":[64],"method":[67],"can":[69],"directly":[70],"use":[71],"data":[72],"with":[73,141,187],"uncertainty":[74],"predict":[76],"behavior":[78],"an":[80],"unknown":[81],"system":[82],"well":[84],"elevate":[86],"speed":[88],"accuracy":[90],"solution":[93,172],"governing":[96],"equations":[97,178],"for":[98,155,174],"known":[99],"systems.":[100],"is":[103,185],"structured":[104],"in":[105,148],"two":[106],"major":[107],"sections.":[108],"In":[109],"first":[111],"section,":[112],"building":[114,164],"blocks":[115,165],"are":[120,139],"presented":[121],"structures":[125],"analogous":[126,194],"traditional":[128],"such":[131],"finite":[133,136],"difference":[134],"element":[137],"constructed":[140],"view":[143],"incorporate":[145],"these":[146],"techniques":[147],"Science,":[149],"Technology,":[150],"Engineering,":[151],"Mathematics":[152],"(STEM)":[153],"syllabus":[154],"K-12":[156],"students.":[157],"second":[159],"section":[160,184],"builds":[161],"upon":[162],"previous":[168],"discussion,and":[169],"new":[171],"schemes":[173],"differential":[175],"integral":[177],"pertinent":[179],"multiscale":[181],"mechanics.":[182],"Each":[183],"accompanied":[186],"mathematical":[188],"formulation":[189],"formulation,":[196],"suitable":[198],"examples.":[199]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2022-12-12T00:00:00"}
