{"id":"https://openalex.org/W7162643303","doi":"https://doi.org/10.48550/arxiv.2605.27756","title":"Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks","display_name":"Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162643303","doi":"https://doi.org/10.48550/arxiv.2605.27756"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.27756","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27756","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.27756","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101766541","display_name":"Tomoki Koike","orcid":"https://orcid.org/0000-0001-5380-3577"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koike, Tomoki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137204298","display_name":"Prakash Mohan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohan, Prakash","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123505339","display_name":"Marc T. Henry de Frahan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de Frahan, Marc T. Henry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137251935","display_name":"Elizabeth Qian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qian, Elizabeth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091899229","display_name":"Julie Bessac","orcid":"https://orcid.org/0000-0001-6407-2423"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bessac, Julie","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9961000084877014,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9961000084877014,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.0003000000142492354,"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/interpretability","display_name":"Interpretability","score":0.6614000201225281},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5853000283241272},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4959000051021576},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48080000281333923},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.44440001249313354},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4381999969482422},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4124999940395355},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.40529999136924744},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4052000045776367}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6614000201225281},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5853000283241272},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5091999769210815},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46790000796318054},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37950000166893005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3781000077724457},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.37059998512268066},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3529999852180481},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.32989999651908875},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C2984998066","wikidata":"https://www.wikidata.org/wiki/Q105037988","display_name":"Proper orthogonal decomposition","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.27219998836517334},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.26980000734329224},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.27756","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27756","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.27756","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27756","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.4829680323600769}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Linear":[0],"dimensionality":[1,128],"reduction":[2,129],"methods":[3,45,83,205],"such":[4,55],"as":[5,56],"proper":[6],"orthogonal":[7],"decomposition":[8],"(POD)":[9],"make":[10],"high-dimensional":[11],"data":[12,32,49],"amenable":[13],"to":[14,76,157,201],"analysis":[15],"by":[16,198],"identifying":[17],"the":[18,25,31,39,101,104],"principal":[19],"components,":[20],"or":[21,28,89,179],"modes,":[22,98],"that":[23,131,167],"capture":[24,77],"most":[26],"variance,":[27],"energy,":[29],"in":[30,38],"and":[33,58,135,162,174],"constructing":[34],"a":[35,107,127,143,149,153,164],"low-dimensional":[36],"representation":[37],"subspace":[40],"they":[41],"span.":[42],"Such":[43],"linear":[44,133,154],"struggle,":[46],"however,":[47],"for":[48,65],"with":[50,87,96,152],"slowly":[51],"decaying":[52],"Kolmogorov":[53],"$n$-widths,":[54],"advection-dominated":[57,173],"turbulent":[59,184],"flows,":[60,176],"which":[61],"require":[62],"many":[63],"modes":[64,74,161],"accurate":[66],"reconstruction;":[67],"moreover,":[68],"energy-based":[69,122],"truncation":[70],"can":[71],"discard":[72],"low-energy":[73],"needed":[75],"small-scale":[78],"features.":[79],"Recent":[80],"nonlinear":[81,105,136,165],"manifold":[82,204],"using":[84],"polynomial":[85,203],"mappings":[86],"alternating":[88],"greedy":[90],"mode":[91,212],"selection":[92],"achieve":[93],"better":[94],"reconstruction":[95,169,196],"fewer":[97],"but":[99],"fix":[100],"form":[102],"of":[103],"mapping":[106,166],"priori,":[108],"limiting":[109],"expressivity.":[110],"In":[111],"contrast,":[112],"neural":[113],"network":[114],"(NN)":[115],"manifolds":[116],"offer":[117],"greater":[118],"expressivity":[119],"yet":[120],"employ":[121],"selection.":[123,213],"We":[124],"present":[125],"SparseModesNet,":[126],"framework":[130],"employs":[132],"encoding":[134],"NN":[137],"decoding.":[138],"The":[139],"decoder":[140],"leverages":[141],"LassoNet,":[142],"method":[144,194],"enforcing":[145],"hierarchical":[146],"sparsity":[147],"through":[148,209],"residual":[150],"connection":[151],"skip":[155],"layer,":[156],"simultaneously":[158],"select":[159],"informative":[160],"learn":[163],"minimizes":[168],"error.":[170],"On":[171],"benchmark":[172],"chaotic":[175],"SparseModesNet":[177],"matches":[178],"exceeds":[180],"state-of-the-art":[181],"performance.":[182],"For":[183],"channel":[185],"flow":[186],"at":[187],"friction":[188],"Reynolds":[189],"number":[190],"$Re_\u03c4=":[191],"5200$,":[192],"our":[193],"reduces":[195],"error":[197],"51-78%":[199],"compared":[200],"existing":[202],"while":[206],"maintaining":[207],"interpretability":[208],"physically":[210],"meaningful":[211]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-29T00:00:00"}
