{"id":"https://openalex.org/W7214917972","doi":"https://doi.org/10.48550/arxiv.2609.37140","title":"BandPC: Learning Residual-Band Preconditioner Combinations for Flexible Conjugate Gradient Solvers","display_name":"BandPC: Learning Residual-Band Preconditioner Combinations for Flexible Conjugate Gradient Solvers","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214917972","doi":"https://doi.org/10.48550/arxiv.2609.37140"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37140","pdf_url":"https://arxiv.org/pdf/2609.37140","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37140","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153584110","display_name":"D. M. Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, D. M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153582591","display_name":"Shang-Tian Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Shang-Tian","raw_affiliation_strings":[". School of Civil Engineering and Architecture , Wuhan University of Technology , Wuhan , 430070 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Civil Engineering and Architecture , Wuhan University of Technology , Wuhan , 430070 , China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153593117","display_name":"Xin Qiu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiu, Xin","raw_affiliation_strings":[". Sanya Science and Education Innovation Park of Wuhan University of Technology , Sanya , 572000 , China",". School of Civil Engineering and Architecture , Wuhan University of Technology , Wuhan , 430070 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". Sanya Science and Education Innovation Park of Wuhan University of Technology , Sanya , 572000 , China","institution_ids":["https://openalex.org/I196699116"]},{"raw_affiliation_string":". School of Civil Engineering and Architecture , Wuhan University of Technology , Wuhan , 430070 , China","institution_ids":["https://openalex.org/I196699116"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/preconditioner-selection","display_name":"preconditioner selection","score":0.7229999899864197},{"id":"https://openalex.org/keywords/graph-neural-networks","display_name":"graph neural networks","score":0.9409999847412109},{"id":"https://openalex.org/keywords/soft-labeling","display_name":"soft labeling","score":0.7620000243186951},{"id":"https://openalex.org/keywords/hierarchical-feature-representation","display_name":"hierarchical feature representation","score":0.7459999918937683},{"id":"https://openalex.org/keywords/iterative-solvers","display_name":"iterative solvers","score":0.7820000052452087}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9354000091552734},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8363999724388123},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.6427000164985657},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.625},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5020999908447266},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46000000834465027},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4544000029563904},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42969998717308044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4043999910354614},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3781000077724457},{"id":"https://openalex.org/C89408827","wikidata":"https://www.wikidata.org/wiki/Q855169","display_name":"Biconjugate gradient method","level":5,"score":0.32690000534057617},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.3149999976158142},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2847000062465668},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2680000066757202},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37140","pdf_url":"https://arxiv.org/pdf/2609.37140","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,"listed_in":[],"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.2609.37140","doi":"https://doi.org/10.48550/arxiv.2609.37140","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37140","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,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37140","pdf_url":"https://arxiv.org/pdf/2609.37140","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,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214917972.pdf","grobid_xml":"https://content.openalex.org/works/W7214917972.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2949278856","https://openalex.org/W4226300991","https://openalex.org/W4378711710","https://openalex.org/W4391767345","https://openalex.org/W4405255071","https://openalex.org/W7021208558","https://openalex.org/W7117305024"],"related_works":["https://openalex.org/W7021208558","https://openalex.org/W7163160542","https://openalex.org/W4415926582","https://openalex.org/W4399062484","https://openalex.org/W2504824111","https://openalex.org/W7100182442","https://openalex.org/W4378711710","https://openalex.org/W7098068031","https://openalex.org/W4405255071","https://openalex.org/W4399399237"],"abstract_inverted_index":{"The":[0],"conjugate":[1,77],"gradient":[2,78],"(CG)":[3],"method":[4],"is":[5],"a":[6,60,92,121,132,144,149,167],"classical":[7,102],"iterative":[8],"solver":[9],"for":[10,74],"sparse":[11],"symmetric":[12],"positive":[13],"definite":[14],"(SPD)":[15],"linear":[16],"systems,":[17],"but":[18],"its":[19],"convergence":[20],"strongly":[21],"depends":[22],"on":[23,166,192],"the":[24,28,75,83,178,185],"spectral":[25],"properties":[26],"of":[27,96,170,196],"system":[29],"matrix.":[30],"Preconditioning":[31],"can":[32,218],"improve":[33,126],"these":[34],"properties;":[35],"however,":[36],"designing":[37],"preconditioners":[38,110],"that":[39,63,135,153,182,213],"generalize":[40],"across":[41,111],"diverse":[42,175],"and":[43,90,128,139,161,174,189,194],"irregular":[44],"sparsity":[45],"patterns":[46],"remains":[47],"challenging.":[48],"We":[49],"propose":[50],"BandPC":[51,81,113,183],"(Band":[52],"Preconditioner":[53],"Combinations,":[54],"where":[55],"\"Band\"":[56],"denotes":[57],"residual-norm":[58],"bands),":[59],"data-driven":[61],"framework":[62],"leverages":[64],"graph":[65],"neural":[66],"networks":[67],"(GNNs)":[68],"to":[69,108,115,120],"predict":[70],"multi-stage":[71],"preconditioning":[72],"strategies":[73],"flexible":[76,221],"(FCG)":[79],"method.":[80],"partitions":[82],"FCG":[84],"iteration":[85,187],"into":[86,143],"three":[87],"residual-norm-based":[88],"bands":[89],"defines":[91],"structured":[93],"search":[94],"space":[95],"125":[97],"candidate":[98],"combinations":[99,138],"over":[100],"five":[101],"preconditioners.":[103],"By":[104],"exploiting":[105],"FCG's":[106],"ability":[107],"switch":[109],"iterations,":[112],"learns":[114],"map":[116],"matrix":[117,163],"structure":[118],"directly":[119],"promising":[122],"preconditioner":[123,216],"sequence.":[124],"To":[125],"training":[127],"generalization,":[129],"we":[130],"introduce":[131],"soft-labeling":[133],"mechanism":[134],"retains":[136],"near-optimal":[137],"normalizes":[140],"their":[141],"scores":[142],"label":[145],"distribution,":[146],"together":[147],"with":[148,203],"hierarchical":[150],"feature":[151],"representation":[152],"captures":[154],"node-level":[155],"attributes,":[156],"edge-level":[157],"algebraic":[158],"coupling":[159],"strengths,":[160],"global":[162],"statistics.":[164],"Experiments":[165],"hybrid":[168],"benchmark":[169],"synthetic":[171],"SPD":[172],"problems":[173],"matrices":[176],"from":[177],"SuiteSparse":[179],"Collection":[180],"show":[181],"achieves":[184],"best":[186,207],"count":[188],"solution":[190],"time":[191],"41.3%":[193],"33.1%":[195],"test":[197],"matrices,":[198],"respectively,":[199],"even":[200],"when":[201],"compared":[202],"each":[204],"matrix's":[205],"individually":[206],"traditional":[208],"preconditioner.":[209],"These":[210],"results":[211],"demonstrate":[212],"learned":[214],"residual-band":[215],"scheduling":[217],"effectively":[219],"accelerate":[220],"CG":[222],"solvers.":[223]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
