{"id":"https://openalex.org/W4389984266","doi":"https://doi.org/10.48550/arxiv.2312.11093","title":"MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids","display_name":"MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids","publication_year":2023,"publication_date":"2023-12-18","ids":{"openalex":"https://openalex.org/W4389984266","doi":"https://doi.org/10.48550/arxiv.2312.11093"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2312.11093","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.11093","pdf_url":"https://arxiv.org/pdf/2312.11093","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":"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/2312.11093","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100385341","display_name":"Yan Xie","orcid":"https://orcid.org/0009-0004-2861-3383"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Yan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106743048","display_name":"Minrui Lv","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lv, Minrui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103156780","display_name":"Chen-Song Zhang","orcid":"https://orcid.org/0000-0002-2213-0899"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Chensong","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":true,"cited_by_count":1,"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":0.9782999753952026,"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":0.9782999753952026,"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":0.9495000243186951,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9038000106811523,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.8890072107315063},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.7475970983505249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6156882643699646},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5798179507255554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5518275499343872},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4923352003097534},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.48128050565719604},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.43155190348625183},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.4282476305961609},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4199422597885132},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3930721580982208},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3668767809867859},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3463594913482666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3150798976421356},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23358869552612305},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.222758948802948},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14416199922561646},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07092428207397461}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.8890072107315063},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.7475970983505249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6156882643699646},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5798179507255554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5518275499343872},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4923352003097534},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.48128050565719604},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.43155190348625183},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.4282476305961609},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4199422597885132},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3930721580982208},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3668767809867859},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3463594913482666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3150798976421356},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23358869552612305},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.222758948802948},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14416199922561646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07092428207397461},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2312.11093","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.11093","pdf_url":"https://arxiv.org/pdf/2312.11093","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.11093","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.11093","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":"pmh:oai:arXiv.org:2312.11093","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.11093","pdf_url":"https://arxiv.org/pdf/2312.11093","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G790494869","display_name":null,"funder_award_id":"XDB0640000","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389984266.pdf","grobid_xml":"https://content.openalex.org/works/W4389984266.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W2146343568","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2013643406","https://openalex.org/W2027972911","https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W288746350"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,34,58,110,174,199],"learnable":[4],"solver":[5,27,129,157,166],"tailored":[6],"to":[7,61,67,81,84,133,170,184,204,215,217],"iteratively":[8],"solve":[9],"sparse":[10],"linear":[11,115],"systems":[12,116],"from":[13,117,180],"discretized":[14,122],"partial":[15],"differential":[16],"equations":[17,160],"(PDEs).":[18],"Unlike":[19],"traditional":[20],"approaches":[21],"relying":[22],"on":[23,89,123,158],"specialized":[24],"expertise,":[25],"our":[26,127,189,208],"streamlines":[28],"the":[29,70,95,100,131,156,192,212],"algorithm":[30],"design":[31],"process":[32],"for":[33],"class":[35],"of":[36,45,72,99,176,201],"PDEs":[37,118],"through":[38],"training,":[39],"which":[40],"requires":[41],"only":[42],"training":[43,146],"data":[44],"coefficient":[46,219],"distributions.":[47],"The":[48,165],"proposed":[49,128],"method":[50,190],"is":[51,147],"anchored":[52],"by":[53],"three":[54],"core":[55],"principles:":[56],"(1)":[57],"multilevel":[59],"hierarchy":[60],"promote":[62],"rapid":[63],"convergence,":[64],"(2)":[65],"adherence":[66],"linearity":[68],"concerning":[69],"right-hand-side":[71,136],"equations,":[73],"and":[74,93,140],"(3)":[75],"weights":[76],"sharing":[77],"across":[78],"different":[79],"levels":[80],"facilitate":[82],"adaptability":[83],"various":[85],"problem":[86],"sizes.":[87],"Built":[88],"these":[90],"foundational":[91],"principles":[92],"considering":[94],"similar":[96],"computation":[97],"pattern":[98],"convolutional":[101],"neural":[102],"network":[103,111],"(CNN)":[104],"as":[105],"multigrid":[106],"components,":[107],"we":[108,154],"introduce":[109],"adept":[112],"at":[113],"solving":[114],"with":[119],"heterogeneous":[120,162],"coefficients,":[121,139],"structured":[124],"grids.":[125],"Notably,":[126],"possesses":[130],"ability":[132],"generalize":[134,216],"over":[135,173],"terms,":[137],"PDE":[138],"grid":[141,177],"sizes,":[142,178],"thereby":[143],"ensuring":[144],"its":[145,152],"purely":[148],"offline.":[149],"To":[150],"evaluate":[151],"effectiveness,":[153],"train":[155],"convection-diffusion":[159],"featuring":[161],"diffusion":[163],"coefficients.":[164],"exhibits":[167],"swift":[168],"convergence":[169],"high":[171],"accuracy":[172],"range":[175],"extending":[179],"$31":[181],"\\times":[182,186],"31$":[183],"$4095":[185],"4095$.":[187],"Remarkably,":[188],"outperforms":[191],"classical":[193],"Geometric":[194],"Multigrid":[195],"(GMG)":[196],"solver,":[197],"demonstrating":[198],"speedup":[200],"approximately":[202],"3":[203],"8":[205],"times.":[206],"Furthermore,":[207],"numerical":[209],"investigation":[210],"into":[211],"solver's":[213],"capacity":[214],"untrained":[218],"distributions":[220],"reveals":[221],"promising":[222],"outcomes.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2023-12-20T00:00:00"}
