{"id":"https://openalex.org/W7166153170","doi":"https://doi.org/10.1109/access.2026.3707535","title":"MSAF-Net: An Adaptive Prediction Model for Shape Parameters in MQ-RBF Interpolation","display_name":"MSAF-Net: An Adaptive Prediction Model for Shape Parameters in MQ-RBF Interpolation","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7166153170","doi":"https://doi.org/10.1109/access.2026.3707535"},"language":"en","primary_location":{"id":"doi:10.1109/access.2026.3707535","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3707535","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2026.3707535","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125189624","display_name":"Ze Song","orcid":null},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ze Song","raw_affiliation_strings":["College of Science, North China University of Science and Technology, Tangshan, China"],"raw_orcid":"https://orcid.org/0009-0007-1068-5743","affiliations":[{"raw_affiliation_string":"College of Science, North China University of Science and Technology, Tangshan, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100398661","display_name":"Ling Wang","orcid":"https://orcid.org/0000-0001-8964-6454"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Wang","raw_affiliation_strings":["College of Science, North China University of Science and Technology, Tangshan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, North China University of Science and Technology, Tangshan, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139414033","display_name":"Dianxuan Gong","orcid":null},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dianxuan Gong","raw_affiliation_strings":["College of Science, North China University of Science and Technology, Tangshan, China"],"raw_orcid":"https://orcid.org/0009-0002-8361-195X","affiliations":[{"raw_affiliation_string":"College of Science, North China University of Science and Technology, Tangshan, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100404947","display_name":"Jie Yang","orcid":"https://orcid.org/0000-0003-4801-7162"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junbo Yang","raw_affiliation_strings":["College of Science, North China University of Science and Technology, Tangshan, China"],"raw_orcid":"https://orcid.org/0009-0004-1490-2037","affiliations":[{"raw_affiliation_string":"College of Science, North China University of Science and Technology, Tangshan, China","institution_ids":["https://openalex.org/I137506752"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137506752"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85482228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"98328","last_page":"98343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.07599999755620956,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.07599999755620956,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.06599999964237213,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"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/T12603","display_name":"NMR spectroscopy and applications","score":0.057999998331069946,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.708899974822998},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.3702000081539154},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.3598000109195709},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.3264000117778778},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.30309998989105225},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.29490000009536743}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.708899974822998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6151000261306763},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4657000005245209},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38280001282691956},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.3702000081539154},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.3598000109195709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3271999955177307},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3043000102043152},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C2984999661","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Surface fitting","level":3,"score":0.26980000734329224},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2583000063896179},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2026.3707535","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3707535","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a3702a802b8f4f27a10ce0c532a97d28","is_oa":false,"landing_page_url":"https://doaj.org/article/a3702a802b8f4f27a10ce0c532a97d28","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,"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":"IEEE Access, Vol 14, Pp 98328-98343 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2026.3707535","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3707535","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1929006416","display_name":null,"funder_award_id":"11601151","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,104],"multiquadric":[1],"radial":[2,60,239],"basis":[3,61,240],"function":[4,62,81],"(MQ-RBF)":[5],"is":[6,29],"widely":[7],"used":[8],"in":[9],"scattered":[10],"data":[11],"interpolation":[12,20,27,64,203],"and":[13,22,43,54,82,85,99,118,125,152,190,202,228],"other":[14,153],"fields":[15],"owing":[16],"to":[17],"its":[18,26],"high":[19,49],"accuracy":[21,201],"broad":[23],"applicability.":[24],"However,":[25],"performance":[28],"highly":[30],"dependent":[31],"on":[32,58],"the":[33,59,70,75,79,114,123,127,131,141,208,220,234],"selection":[34,213,222],"of":[35,78,122,130,160,166,173,181,188,196,210,223,237],"shape":[36,83,132,226],"parameters,":[37,84,227],"whereas":[38],"traditional":[39,211],"methods":[40],"including":[41,148],"trial-and-error":[42],"optimization":[44,236],"algorithms,":[45],"often":[46],"suffer":[47],"from":[48],"computational":[50],"complexity,":[51],"limited":[52],"robustness,":[53],"poor":[55],"adaptability.":[56],"Based":[57],"(RBF)":[63],"error":[65,171,179,186],"theory,":[66],"this":[67],"study":[68],"explores":[69],"nonlinear":[71,111],"coupling":[72],"relationship":[73],"between":[74],"geometric":[76,107],"features":[77],"target":[80],"proposes":[86],"a":[87,95,158,168,175,183,191,216,230],"deep":[88],"learning-based":[89],"multi-scale":[90],"dual-branch":[91],"fusion":[92],"network":[93,98],"with":[94,198],"convolutional":[96],"neural":[97],"an":[100],"attention":[101],"mechanism":[102],"(MSAF-Net).":[103],"model":[105],"extracts":[106],"features,":[108],"enhances":[109],"their":[110],"representations,":[112],"captures":[113],"global":[115],"morphological":[116],"laws":[117],"local":[119],"fine-scale":[120],"information":[121],"function,":[124],"realizes":[126],"direct":[128],"prediction":[129,200],"parameter":[133,212,235],"through":[134],"feature":[135],"fusion.":[136],"Experimental":[137],"results":[138],"demonstrate":[139],"that":[140],"proposed":[142],"MSAF-Net":[143],"significantly":[144],"outperforms":[145],"comparative":[146],"models":[147],"Stacking,":[149],"MLP-XGBoost,":[150],"RF":[151],"baseline":[154],"methods.":[155],"It":[156],"achieves":[157],"coefficient":[159],"determination":[161],"(<inline-formula>":[162],"<tex-math":[163],"notation=\"LaTeX\">$R^{2}$":[164],"</tex-math></inline-formula>)":[165],"0.8887,":[167],"mean":[169,177,184],"squared":[170],"(MSE)":[172],"0.1422,":[174],"root":[176],"square":[178],"(RMSE)":[180],"0.3771,":[182],"absolute":[185],"(MAE)":[187],"0.1400,":[189],"relative":[192],"predictive":[193],"deviation":[194],"(RPD)":[195],"2.997,":[197],"superior":[199],"stability.":[204],"This":[205],"method":[206],"overcomes":[207],"limitations":[209],"strategies,":[214],"provides":[215],"new":[217],"scheme":[218],"for":[219,233],"adaptive":[221],"one-dimensional":[224],"MQ-RBF":[225],"offers":[229],"valuable":[231],"reference":[232],"similar":[238],"functions.":[241]},"counts_by_year":[],"updated_date":"2026-07-04T06:09:54.619538","created_date":"2026-06-27T00:00:00"}
