{"id":"https://openalex.org/W4417267269","doi":"https://doi.org/10.48550/arxiv.2507.19744","title":"An inverse random diffraction grating problem for the Helmholtz equation","display_name":"An inverse random diffraction grating problem for the Helmholtz equation","publication_year":2025,"publication_date":"2025-07-26","ids":{"openalex":"https://openalex.org/W4417267269","doi":"https://doi.org/10.48550/arxiv.2507.19744"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.19744","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19744","pdf_url":"https://arxiv.org/pdf/2507.19744","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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.19744","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Sun, Zhiqi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Zhiqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Lin, Yiwen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Yiwen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11205","display_name":"Numerical methods in inverse problems","score":0.6553999781608582,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.6553999781608582,"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"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.17960000038146973,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.04580000042915344,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/randomness","display_name":"Randomness","score":0.6413000226020813},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5026999711990356},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4580000042915344},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.4120999872684479},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4097000062465668},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.3919000029563904},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.38339999318122864},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.3580999970436096},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.35370001196861267},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.3467999994754791}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6424000263214111},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6413000226020813},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5026999711990356},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4108000099658966},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4011000096797943},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3919000029563904},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35370001196861267},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.3467999994754791},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.34060001373291016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33869999647140503},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.29120001196861267},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.19744","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19744","pdf_url":"https://arxiv.org/pdf/2507.19744","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.19744","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.19744","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.19744","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19744","pdf_url":"https://arxiv.org/pdf/2507.19744","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,43,46,63,71,74,87,119,128,136,172],"inverse":[4],"scattering":[5],"problem":[6],"of":[7,45,73,86,100,109,118,139],"time-harmonic":[8],"plane":[9],"waves":[10],"incident":[11],"on":[12,123,174],"a":[13,36,66,91,98,101,105,149],"perfectly":[14],"reflecting":[15],"random":[16,21,78,88,120,141],"periodic":[17],"structure.":[18],"To":[19],"simulate":[20],"perturbations":[22],"arising":[23],"from":[24],"manufacturing":[25],"defects":[26],"and":[27,56,104,148,177],"surface":[28,38,79,89],"wear":[29],"in":[30,171],"real-world":[31],"grating":[32],"profiles,":[33],"we":[34,126],"propose":[35],"stochastic":[37],"modeling":[39],"framework":[40],"motivated":[41],"by":[42],"discretization":[44],"Wiener":[47,75],"process.":[48],"Our":[49],"approach":[50],"introduces":[51],"randomness":[52],"at":[53],"discrete":[54],"nodes":[55],"then":[57],"applies":[58],"linear":[59,107],"interpolation":[60],"to":[61,69,134],"construct":[62],"surface,":[64],"marking":[65],"novel":[67],"attempt":[68],"incorporate":[70],"concepts":[72],"process":[76],"into":[77],"representation.":[80],"Under":[81],"this":[82,124],"framework,":[83],"each":[84],"realization":[85],"generates":[90],"Lipschitz-continuous":[92],"diffraction":[93],"grating,":[94],"mathematically":[95],"represented":[96],"as":[97],"sum":[99],"baseline":[102],"profile":[103],"weighted":[106],"combination":[108],"local":[110],"`tent'":[111],"basis":[112],"functions,":[113],"meanwhile":[114],"preserving":[115],"key":[116,137],"statistics":[117,138],"surface.":[121],"Building":[122],"representation,":[125],"introduce":[127],"Recursive":[129],"Parametric":[130],"Smoothing":[131],"Strategy":[132],"(RPSS)":[133],"invert":[135],"our":[140,153],"surfaces.":[142],"Combined":[143],"with":[144,168],"Monte":[145],"Carlo":[146],"sampling":[147],"wavenumber":[150],"continuation":[151],"strategy,":[152],"reconstruction":[154,175],"scheme":[155],"demonstrates":[156],"effectiveness":[157],"across":[158],"multiple":[159],"benchmark":[160],"scenarios.":[161],"Several":[162],"numerical":[163],"results":[164],"are":[165],"presented":[166],"along":[167],"some":[169],"discussions":[170],"end":[173],"mechanisms":[176],"future":[178],"extensions.":[179]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
