{"id":"https://openalex.org/W7214166240","doi":"https://doi.org/10.1177/00368504261486725","title":"Neural network-based computational analysis of pressure-driven nonlinear waves in gas\u2013liquid mixtures and oil transportation pipelines","display_name":"Neural network-based computational analysis of pressure-driven nonlinear waves in gas\u2013liquid mixtures and oil transportation pipelines","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7214166240","doi":"https://doi.org/10.1177/00368504261486725","pmid":"https://pubmed.ncbi.nlm.nih.gov/42784463","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/13735666"},"language":"en","primary_location":{"id":"doi:10.1177/00368504261486725","doi":"https://doi.org/10.1177/00368504261486725","is_oa":true,"landing_page_url":"https://doi.org/10.1177/00368504261486725","pdf_url":null,"source":{"id":"https://openalex.org/S9683234","display_name":"Science Progress","issn_l":"0036-8504","issn":["0036-8504","2047-7163"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","medline","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science Progress","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1177/00368504261486725","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091807777","display_name":"Turke Althobaiti","orcid":"https://orcid.org/0000-0002-6674-7890","observed_orcids":["https://orcid.org/0000-0002-6674-7890","https://orcid.org/0009-0007-4540-1990"]},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Turke Althobaiti","raw_affiliation_strings":["Northern Border University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northern Border University","institution_ids":["https://openalex.org/I118590987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092212585","display_name":"Noman Sharif","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Noman Sharif","raw_affiliation_strings":["University of Okara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Okara","institution_ids":["https://openalex.org/I3130814776"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030262365","display_name":"Daba Meshesha Gusu","orcid":"https://orcid.org/0000-0002-5373-6463","observed_orcids":["https://orcid.org/0000-0002-5373-6463","https://orcid.org/0009-0000-2485-181X"]},"institutions":[{"id":"https://openalex.org/I4210114632","display_name":"Ambo University","ror":"https://ror.org/02e6z0y17","country_code":"ET","type":"education","lineage":["https://openalex.org/I4210114632"]}],"countries":["ET"],"is_corresponding":true,"raw_author_name":"Daba Meshesha Gusu","raw_affiliation_strings":["Ambo University"],"raw_orcid":"https://orcid.org/0009-0000-2485-181X","affiliations":[{"raw_affiliation_string":"Ambo University","institution_ids":["https://openalex.org/I4210114632"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027405619","display_name":"Ifrah Iqbal","orcid":"https://orcid.org/0009-0004-6762-9580","observed_orcids":["https://orcid.org/0009-0004-6762-9580"]},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ifrah Iqbal","raw_affiliation_strings":["University of Okara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Okara","institution_ids":["https://openalex.org/I3130814776"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127343066","display_name":"Hamood Ur Rehman","orcid":"https://orcid.org/0000-0002-7338-6288","observed_orcids":["https://orcid.org/0000-0002-7338-6288"]},"institutions":[{"id":"https://openalex.org/I113330528","display_name":"Khazar University","ror":"https://ror.org/014te7048","country_code":"AZ","type":"education","lineage":["https://openalex.org/I113330528"]},{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["AZ","PK"],"is_corresponding":false,"raw_author_name":"Hamood Ur Rehman","raw_affiliation_strings":["Khazar University","University of Okara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khazar University","institution_ids":["https://openalex.org/I113330528"]},{"raw_affiliation_string":"University of Okara","institution_ids":["https://openalex.org/I3130814776"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136751849","display_name":"Yakup Yildirim","orcid":"https://orcid.org/0000-0003-4443-3337","observed_orcids":["https://orcid.org/0000-0003-4443-3337"]},"institutions":[{"id":"https://openalex.org/I4210104933","display_name":"Biruni University","ror":"https://ror.org/01nkhmn89","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210104933"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Yakup Yildirim","raw_affiliation_strings":["Biruni University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biruni University","institution_ids":["https://openalex.org/I4210104933"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5030262365"],"corresponding_institution_ids":["https://openalex.org/I4210114632"],"apc_list":{"value":2650,"currency":"USD","value_usd":2650},"apc_paid":{"value":2650,"currency":"USD","value_usd":2650},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.66123413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"109","issue":"3","first_page":"368504261486725","last_page":"368504261486725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9970999956130981,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9970999956130981,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kudryashov-sinelshchikov-equation","display_name":"Kudryashov-Sinelshchikov equation","score":0.9950000047683716},{"id":"https://openalex.org/keywords/longitudinal-waves","display_name":"longitudinal waves","score":0.6140000224113464},{"id":"https://openalex.org/keywords/bubbly-liquids","display_name":"bubbly liquids","score":0.828000009059906},{"id":"https://openalex.org/keywords/gas-liquid-mixtures","display_name":"gas-liquid mixtures","score":0.968999981880188},{"id":"https://openalex.org/keywords/oil-pipeline-transportation","display_name":"oil pipeline transport","score":0.8379999995231628},{"id":"https://openalex.org/keywords/multiphase-flow","display_name":"multiphase flow","score":0.8159999847412109},{"id":"https://openalex.org/keywords/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.7789999842643738},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.7879999876022339},{"id":"https://openalex.org/keywords/feedforward-neural-networks","display_name":"feedforward neural networks","score":0.621999979019165},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"symbolic computation","score":0.6759999990463257},{"id":"https://openalex.org/keywords/modulational-instability","display_name":"modulational instability","score":0.9599999785423279},{"id":"https://openalex.org/keywords/nonlinear-acoustics","display_name":"nonlinear acoustics","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7671999931335449},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7221999764442444},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5091000199317932},{"id":"https://openalex.org/C175309249","wikidata":"https://www.wikidata.org/wiki/Q725864","display_name":"Pipeline transport","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44279998540878296},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41679999232292175},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35679998993873596},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.3452000021934509},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.3449000120162964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3391000032424927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33559998869895935},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C2779379648","wikidata":"https://www.wikidata.org/wiki/Q1559665","display_name":"Multiphase flow","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1177/00368504261486725","doi":"https://doi.org/10.1177/00368504261486725","is_oa":true,"landing_page_url":"https://doi.org/10.1177/00368504261486725","pdf_url":null,"source":{"id":"https://openalex.org/S9683234","display_name":"Science Progress","issn_l":"0036-8504","issn":["0036-8504","2047-7163"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","medline","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science Progress","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13735666","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13735666/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13735666/pdf/10.1177_00368504261486725.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sci Prog","raw_type":"Text"},{"id":"pmid:42784463","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42784463","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science progress","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:4fb4681f4018480d89fabe2128cdf28a","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/4fb4681f4018480d89fabe2128cdf28a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Science Progress, Vol 109 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1177/00368504261486725","doi":"https://doi.org/10.1177/00368504261486725","is_oa":true,"landing_page_url":"https://doi.org/10.1177/00368504261486725","pdf_url":null,"source":{"id":"https://openalex.org/S9683234","display_name":"Science Progress","issn_l":"0036-8504","issn":["0036-8504","2047-7163"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","medline","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science Progress","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328654","display_name":"Northern Border University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214166240.pdf","grobid_xml":"https://content.openalex.org/works/W7214166240.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W2019438465","https://openalex.org/W2050639649","https://openalex.org/W2053833421","https://openalex.org/W2069763315","https://openalex.org/W2079031520","https://openalex.org/W2118575947","https://openalex.org/W2899283552","https://openalex.org/W3163993681","https://openalex.org/W4213132260","https://openalex.org/W4232650420","https://openalex.org/W4408290539","https://openalex.org/W4409180720","https://openalex.org/W4411707157","https://openalex.org/W4412003471","https://openalex.org/W4414032454","https://openalex.org/W4415406338","https://openalex.org/W4416614334","https://openalex.org/W7126410910","https://openalex.org/W7140159145"],"related_works":["https://openalex.org/W7128311435","https://openalex.org/W7161286559","https://openalex.org/W7160701041","https://openalex.org/W3197436794","https://openalex.org/W4414223866","https://openalex.org/W7216435773","https://openalex.org/W4416614334","https://openalex.org/W7154944274","https://openalex.org/W7196966255","https://openalex.org/W7202137631"],"abstract_inverted_index":{"In":[0,55,94,161],"this":[1],"work,":[2],"we":[3,59],"develop":[4],"a":[5,18,28,64,203],"computational":[6],"approach":[7],"for":[8,120,207],"the":[9,13,23,38,56,61,71,80,91,102,128,133,137,141,144,149,171,177,192],"analytical":[10],"investigation":[11],"of":[12,15,33,40,63,90,112,127,143,151,173,211],"dynamics":[14],"waves":[16,42],"in":[17,43,136,158,191],"nonlinear":[19,29,53,212],"system":[20],"described":[21],"by":[22,110,132],"Kudryashov-Sinelshchikov":[24],"equation":[25,32,83],"which":[26],"is":[27,84,117,130,166,183,187],"partial":[30],"differential":[31],"(1+1)":[34],"dimensions":[35],"that":[36,185],"models":[37],"propagation":[39],"pressure":[41],"bubbly":[44],"liquids,":[45],"multiphase":[46],"flow":[47],"systems,":[48],"oil":[49],"pipeline":[50],"transport,":[51],"and":[52,70,115,154,181],"acoustics.":[54],"suggested":[57,196],"approach,":[58],"use":[60],"combination":[62],"multilayer":[65],"feedforward":[66],"artificial":[67,99],"neural":[68,100,104,197],"network":[69,105],"Riccati":[72,81],"sub-equation":[73],"method":[74],"where":[75],"an":[76,87],"exact":[77,209],"solution":[78],"to":[79,96,169],"auxiliary":[82],"used":[85],"as":[86,202],"activation":[88],"function":[89],"hidden":[92],"layer.":[93],"contrast":[95],"typical":[97],"data-driven":[98],"networks,":[101],"unknown":[103],"parameters":[106],"are":[107,146],"calculated":[108],"analytically":[109],"means":[111],"symbolic":[113],"computations,":[114],"there":[116,186],"no":[118,188],"need":[119],"training":[121],"or":[122],"optimization":[123],"procedures.":[124],"The":[125,195],"validity":[126],"solutions":[129,145,193,210],"checked":[131],"direct":[134],"substitution":[135],"governing":[138],"equation,":[139],"while":[140],"properties":[142],"analyzed":[147],"with":[148],"help":[150],"two,":[152],"three,":[153],"contour":[155],"plots":[156],"constructed":[157],"Wolfram":[159],"Mathematica.":[160],"addition,":[162],"modulation":[163],"instability":[164,190],"analysis":[165],"carried":[167],"out":[168],"study":[170],"effect":[172],"small":[174],"perturbation":[175],"on":[176],"continuous":[178],"wave":[179],"solutions,":[180],"it":[182],"found":[184],"exponential":[189],"obtained.":[194],"network-inspired":[198],"theoretical":[199],"model":[200],"serves":[201],"computationally":[204],"effective":[205],"tool":[206],"finding":[208],"evolution":[213],"equations.":[214]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-25T00:00:00"}
