{"id":"https://openalex.org/W3111082652","doi":"https://doi.org/10.1137/19m1294484","title":"Convolutional Neural Networks in Phase Space and Inverse Problems","display_name":"Convolutional Neural Networks in Phase Space and Inverse Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3111082652","doi":"https://doi.org/10.1137/19m1294484","mag":"3111082652"},"language":"en","primary_location":{"id":"doi:10.1137/19m1294484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294484","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied 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/A5109171815","display_name":"G\u00fcnther Uhlmann","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK","US"],"is_corresponding":true,"raw_author_name":"Gunther Uhlmann","raw_affiliation_strings":["Department of Mathematics, Stanford University","Department of Mathematics, University of Washington and Institute for Advanced Study, the Hong Kong University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington and Institute for Advanced Study, the Hong Kong University of Science and Technology","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I40036882","https://openalex.org/I200769079","https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101650033","display_name":"Yiran Wang","orcid":"https://orcid.org/0000-0001-5069-0538"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Yiran Wang","raw_affiliation_strings":["Department of Mathematics, Stanford University","Department of Mathematics, University of Washington and Institute for Advanced Study, the Hong Kong University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington and Institute for Advanced Study, the Hong Kong University of Science and Technology","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I40036882","https://openalex.org/I200769079","https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109171815"],"corresponding_institution_ids":["https://openalex.org/I200769079","https://openalex.org/I201448701","https://openalex.org/I40036882","https://openalex.org/I889458895","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.1717,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.47568479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"80","issue":"6","first_page":"2560","last_page":"2585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/convolutional-neural-network","display_name":"Convolutional neural network","score":0.7722161412239075},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6814371943473816},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6258819103240967},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.621439516544342},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5473138093948364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5439231395721436},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5174765586853027},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4978299140930176},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.46991032361984253},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4697972238063812},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4230929911136627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3899475634098053},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38716116547584534},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3355870544910431},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33550137281417847},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3105626702308655},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22940251231193542},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12020501494407654}],"concepts":[{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.7722161412239075},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6814371943473816},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6258819103240967},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.621439516544342},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5473138093948364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5439231395721436},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5174765586853027},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4978299140930176},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.46991032361984253},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4697972238063812},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4230929911136627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3899475634098053},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38716116547584534},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3355870544910431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33550137281417847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3105626702308655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22940251231193542},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12020501494407654},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1294484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294484","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-108368","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-108368","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-108368","is_oa":false,"landing_page_url":"http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=0036-1399&rft.volume=v. 80&rft.issue=(6)&rft.date=2020&rft.spage=2560&rft.aulast=Uhlmann&rft.aufirst=Gunther&rft.atitle=CONVOLUTIONAL+NEURAL+NETWORKS+IN+PHASE+SPACE+AND+INVERSE+PROBLEMS&rft.title=SIAM+JOURNAL+ON+APPLIED+MATHEMATICS","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310094","display_name":"University of Washington","ror":"https://ror.org/00cvxb145"},{"id":"https://openalex.org/F4320323537","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1489373617","https://openalex.org/W1965632887","https://openalex.org/W1976007818","https://openalex.org/W1982479117","https://openalex.org/W1994906459","https://openalex.org/W2012701400","https://openalex.org/W2027197837","https://openalex.org/W2032190612","https://openalex.org/W2134972164","https://openalex.org/W2137983211","https://openalex.org/W2261689926","https://openalex.org/W2327023604","https://openalex.org/W2335653873","https://openalex.org/W2899283552","https://openalex.org/W2919115771","https://openalex.org/W2963238585","https://openalex.org/W2963681095","https://openalex.org/W2964318021","https://openalex.org/W2964318119","https://openalex.org/W2974916071","https://openalex.org/W2998069873","https://openalex.org/W3106050203","https://openalex.org/W3125537303"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W1976205134","https://openalex.org/W2381570729","https://openalex.org/W4248336175","https://openalex.org/W3009369890","https://openalex.org/W2331917905","https://openalex.org/W3155039083","https://openalex.org/W1543136835","https://openalex.org/W4210375670"],"abstract_inverted_index":{"We":[0],"study":[1],"inverse":[2],"problems":[3],"consisting":[4],"of":[5,20,26,28,45,65,67,77],"determining":[6],"medium":[7,52],"properties":[8],"using":[9],"the":[10,16,24,43,51,61,68,75,78],"responses":[11],"to":[12,41],"probing":[13],"waves":[14,29],"from":[15],"machine":[17],"learning":[18],"point":[19],"view.":[21],"Based":[22],"on":[23,74],"analysis":[25],"propagation":[27],"and":[30,63,70],"their":[31,71],"nonlinear":[32,46],"interactions,":[33],"we":[34,59],"construct":[35],"a":[36],"deep":[37],"convolutional":[38],"neural":[39],"network":[40,69],"reconstruct":[42],"coefficients":[44],"wave":[47],"equations":[48],"that":[49],"model":[50],"properties.":[53],"Furthermore,":[54],"for":[55],"given":[56],"approximation":[57],"accuracy,":[58],"obtain":[60],"depth":[62],"number":[64],"units":[66],"quantitative":[72],"dependence":[73],"complexity":[76],"medium.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}