{"id":"https://openalex.org/W7204164990","doi":"https://doi.org/10.48550/arxiv.2608.22592","title":"Error attribution in gradient random walk methods for parabolic equations","display_name":"Error attribution in gradient random walk methods for parabolic equations","publication_year":2026,"publication_date":"2026-08-23","ids":{"openalex":"https://openalex.org/W7204164990","doi":"https://doi.org/10.48550/arxiv.2608.22592"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.22592","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22592","pdf_url":"https://arxiv.org/pdf/2608.22592","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/2608.22592","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147697945","display_name":"Stephen Abkin","orcid":"https://orcid.org/0009-0000-5981-9721","observed_orcids":["https://orcid.org/0009-0000-5981-9721"]},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abkin, Stephen","raw_affiliation_strings":["Department of Mathematics Texas A&M University College Station , TX , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Texas A&M University College Station , TX , USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034954097","display_name":"Prabir K. Daripa","orcid":"https://orcid.org/0000-0002-8771-0149","observed_orcids":["https://orcid.org/0000-0002-8771-0149"]},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daripa, Prabir","raw_affiliation_strings":["Department of Mathematics Texas A&M University College Station , TX , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Texas A&M University College Station , TX , USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91045830"],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.12280000001192093,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.12280000001192093,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.1151999980211258,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.08810000121593475,"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/parabolic-partial-differential-equations","display_name":"parabolic equations","score":0.7730000019073486},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.781000018119812},{"id":"https://openalex.org/keywords/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.8519999980926514},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers equation","score":0.9700000286102295},{"id":"https://openalex.org/keywords/error-analysis","display_name":"error analysis","score":0.6700000166893005},{"id":"https://openalex.org/keywords/particle-methods","display_name":"particle methods","score":0.41999998688697815},{"id":"https://openalex.org/keywords/cole-hopf-transformation","display_name":"Cole-Hopf transformation","score":0.7960000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6800000071525574},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6123999953269958},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5752999782562256},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40380001068115234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3955000042915344},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3693999946117401},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C154072304","wikidata":"https://www.wikidata.org/wiki/Q5747218","display_name":"Heterogeneous random walk in one dimension","level":3,"score":0.30630001425743103},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2996000051498413},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.27059999108314514},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.22592","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22592","pdf_url":"https://arxiv.org/pdf/2608.22592","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.2608.22592","doi":"https://doi.org/10.48550/arxiv.2608.22592","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.22592","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:2608.22592","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22592","pdf_url":"https://arxiv.org/pdf/2608.22592","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204164990.pdf","grobid_xml":"https://content.openalex.org/works/W7204164990.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1483246486","https://openalex.org/W1555627060","https://openalex.org/W1964404845","https://openalex.org/W1992906507","https://openalex.org/W1995623318","https://openalex.org/W2001839279","https://openalex.org/W2009375605","https://openalex.org/W2012050842","https://openalex.org/W2012189899","https://openalex.org/W2045384647","https://openalex.org/W2052582477","https://openalex.org/W2061191702","https://openalex.org/W2107190127","https://openalex.org/W2124148066","https://openalex.org/W2565432921","https://openalex.org/W3048432586","https://openalex.org/W3109759543","https://openalex.org/W4244063180","https://openalex.org/W4312354951","https://openalex.org/W4376861984","https://openalex.org/W4400563965"],"related_works":["https://openalex.org/W7097655756","https://openalex.org/W2737167921","https://openalex.org/W2012050842","https://openalex.org/W3207779525","https://openalex.org/W1995623318","https://openalex.org/W2011991749","https://openalex.org/W3021760708","https://openalex.org/W2079560423","https://openalex.org/W3198172059","https://openalex.org/W2583765376"],"abstract_inverted_index":{"Gradient":[0],"random":[1],"walk":[2],"(GRW)":[3],"methods":[4],"represent":[5],"a":[6,61,91,98],"solution's":[7],"spatial":[8],"derivative":[9],"by":[10,17],"weighted":[11],"particles":[12],"and":[13,31,38,71,86,114],"recover":[14],"the":[15,25,42,50,66,78,83,87,128],"solution":[16],"cumulative":[18,54],"summation.":[19],"We":[20],"examine":[21],"their":[22,139],"accuracy":[23,47],"for":[24,77,90],"one-dimensional":[26],"heat,":[27],"scalar":[28],"cubic":[29],"reaction-diffusion,":[30],"Burgers'":[32,121],"equations.":[33],"Thirty-seed":[34],"ensembles,":[35],"paired":[36],"reconstructions,":[37],"deterministic":[39,129,140],"controls":[40],"identify":[41],"sources":[43],"of":[44,108],"two":[45],"apparent":[46],"limits.":[48],"For":[49,120],"heat":[51],"equation,":[52,122],"comparing":[53],"bin":[55,58],"sums":[56],"at":[57],"centers":[59],"introduces":[60],"first-order":[62],"alignment":[63],"error,":[64],"which":[65],"exact":[67,123],"reflected-particle":[68],"distribution":[69],"predicts":[70,82],"bin-edge":[72],"comparison":[73],"removes.":[74],"An":[75],"identity":[76],"expected":[79],"squared":[80],"error":[81,105,131],"remaining":[84],"floor":[85],"particle":[88,136],"count":[89,99],"target":[92],"root-mean-square":[93],"accuracy.":[94],"With":[95],"unequal":[96],"weights,":[97],"chosen":[100],"in":[101],"advance":[102],"gives":[103],"an":[104],"within":[106],"1%":[107],"its":[109],"prediction.":[110],"Reaction-front":[111],"position,":[112],"speed,":[113],"shape":[115],"errors":[116],"decrease":[117],"under":[118],"refinement.":[119],"transformed":[124],"boundary":[125],"data":[126],"reduce":[127],"Cole-Hopf":[130],"about":[132],"490-fold,":[133],"while":[134],"fixed-endpoint":[135],"runs":[137],"approach":[138],"reference.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-26T00:00:00"}
