{"id":"https://openalex.org/W7160501223","doi":"https://doi.org/10.48550/arxiv.2605.04918","title":"Neural Discovery of Strichartz Extremizers","display_name":"Neural Discovery of Strichartz Extremizers","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160501223","doi":"https://doi.org/10.48550/arxiv.2605.04918"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04918","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04918","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.04918","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135559618","display_name":"Nicol\u00e1s Valenzuela","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Valenzuela, Nicol\u00e1s","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135591196","display_name":"Ricardo Freire","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Freire, Ricardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006963626","display_name":"Claudio Mu\u00f1oz","orcid":"https://orcid.org/0000-0002-9029-2005"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mu\u00f1oz, Claudio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.4374000132083893,"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"}},"topics":[{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.4374000132083893,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.05530000105500221,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.04560000076889992,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/iterated-function","display_name":"Iterated function","score":0.7350000143051147},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.7125999927520752},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.489300012588501},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4867999851703644},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.48590001463890076},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46209999918937683}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7350000143051147},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.7125999927520752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6640999913215637},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46209999918937683},{"id":"https://openalex.org/C74455749","wikidata":"https://www.wikidata.org/wiki/Q5254599","display_name":"Breather","level":3,"score":0.4431999921798706},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42989999055862427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36809998750686646},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2700999975204468},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2612000107765198}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04918","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04918","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.04918","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04918","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6128845810890198,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Strichartz":[0,61],"inequalities":[1],"are":[2,15,118],"a":[3,20,48,176,192,216,223],"cornerstone":[4],"of":[5,9,22,27,59,79],"the":[6,28,32,60,71,76,104,108,114,119,123,128,138,148,162,166,182,195,207],"modern":[7],"theory":[8],"dispersive":[10],"PDEs,":[11],"but":[12,203],"their":[13],"extremizers":[14,55,78,121],"known":[16,219],"explicitly":[17],"only":[18],"in":[19,66,83,101,122],"handful":[21],"sharp":[23],"cases.":[24],"The":[25,210],"non-convexity":[26],"underlying":[29],"functional":[30],"makes":[31],"problem":[33],"hard,":[34],"and":[35,63,81,161,200,221],"to":[36,86,143],"our":[37],"knowledge":[38],"no":[39,92,227],"systematic":[40],"numerical":[41],"attack":[42],"has":[43],"been":[44],"attempted.":[45],"We":[46,180,190],"propose":[47,191],"simple":[49],"neural-network-based":[50],"pipeline":[51,211],"that":[52,116],"searches":[53],"for":[54],"as":[56,152,215,222],"critical":[57,129],"points":[58],"ratio,":[62],"apply":[64],"it":[65],"three":[67],"settings.":[68],"First,":[69],"on":[70,96,127,218],"Schr\u00f6dinger":[72],"group":[73],"we":[74],"recover":[75],"Gaussian":[77],"Foschi":[80],"Hundertmark--Zharnitsky":[82],"dimensions":[84],"$d=1,2$":[85],"within":[87],"$10^{-3}$":[88],"relative":[89],"error,":[90],"with":[91,156,175,185],"analytical":[93],"prior.":[94],"Second,":[95],"$59$":[97],"further":[98],"admissible":[99,124],"pairs":[100],"$d=1$":[102],"where":[103,134],"answer":[105],"is":[106,136,201],"conjectural,":[107],"method":[109],"consistently":[110],"finds":[111],"Gaussians,":[112],"supporting":[113],"conjecture":[115],"Gaussians":[117],"universal":[120,168],"range.":[125],"Third,":[126],"Airy--Strichartz":[130],"inequality":[131],"at":[132],"$\u03b3=1/q$,":[133],"existence":[135],"open,":[137],"optimization":[139],"does":[140],"not":[141,204],"converge":[142],"any":[144],"$L^2$":[145],"profile:":[146],"instead,":[147],"iterates":[149],"organize":[150],"themselves":[151],"mKdV":[153],"breathers":[154],"$B(0,\\cdot;\u03b1,1,0,0)$":[155],"growing":[157],"internal":[158],"frequency":[159],"$\u03b1$,":[160],"discovered":[163],"ratio":[164],"approaches":[165],"Frank--Sabin":[167],"lower":[169],"bound":[170],"$\\widetilde":[171,198],"A_{q,r}$":[172,199],"from":[173],"below":[174],"power-law":[177],"gap":[178],"$\\sim\u03b1^{-0.9}$.":[179],"confirm":[181],"same":[183],"picture":[184],"an":[186],"independent":[187],"Hermite-basis":[188],"ansatz.":[189],"precise":[193],"conjecture:":[194],"supremum":[196],"equals":[197],"approached,":[202],"attained,":[205],"along":[206],"breather":[208],"family.":[209],"thus":[212],"serves":[213],"both":[214],"validator":[217],"cases":[220],"discovery":[224],"tool":[225],"when":[226],"extremizer":[228],"exists.":[229]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-08T00:00:00"}