{"id":"https://openalex.org/W4416199658","doi":"https://doi.org/10.3390/e27111155","title":"Supervised and Unsupervised Learning with Numerical Computation for the Wolfram Cellular Automata","display_name":"Supervised and Unsupervised Learning with Numerical Computation for the Wolfram Cellular Automata","publication_year":2025,"publication_date":"2025-11-14","ids":{"openalex":"https://openalex.org/W4416199658","doi":"https://doi.org/10.3390/e27111155","pmid":"https://pubmed.ncbi.nlm.nih.gov/41294998"},"language":"en","primary_location":{"id":"doi:10.3390/e27111155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111155","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1155/pdf?version=1763114454","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/11/1155/pdf?version=1763114454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092950313","display_name":"Kui Tuo","orcid":null},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kui Tuo","raw_affiliation_strings":["Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074204060","display_name":"Shengfeng Deng","orcid":"https://orcid.org/0000-0002-1952-8599"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengfeng Deng","raw_affiliation_strings":["School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710061, China","School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710061, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710061, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuxiang Yang","orcid":"https://orcid.org/0009-0000-9069-0591"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuxiang Yang","raw_affiliation_strings":["Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China"],"raw_orcid":"https://orcid.org/0009-0000-9069-0591","affiliations":[{"raw_affiliation_string":"Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101821032","display_name":"Y. Wang","orcid":"https://orcid.org/0009-0003-9852-176X"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanyang Wang","raw_affiliation_strings":["Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China"],"raw_orcid":"https://orcid.org/0009-0003-9852-176X","affiliations":[{"raw_affiliation_string":"Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100652139","display_name":"Qiuping Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I58581550","display_name":"Institut Polytechnique des Sciences Avanc\u00e9es","ror":"https://ror.org/050r7zc91","country_code":"FR","type":"education","lineage":["https://openalex.org/I58581550"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Qiuping Wang","raw_affiliation_strings":["Laboratoire Syst\u00e8mes Complexes et Information Quantique (SCIQ) Lab, ESIEA, 74 bis Avenue Maurice Thorez, 94200 Ivry sur Seine, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Syst\u00e8mes Complexes et Information Quantique (SCIQ) Lab, ESIEA, 74 bis Avenue Maurice Thorez, 94200 Ivry sur Seine, France","institution_ids":["https://openalex.org/I58581550"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100317994","display_name":"Wei Li","orcid":"https://orcid.org/0000-0001-7015-7335"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]},{"id":"https://openalex.org/I58581550","display_name":"Institut Polytechnique des Sciences Avanc\u00e9es","ror":"https://ror.org/050r7zc91","country_code":"FR","type":"education","lineage":["https://openalex.org/I58581550"]}],"countries":["CN","FR"],"is_corresponding":true,"raw_author_name":"Wei Li","raw_affiliation_strings":["Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China","Laboratoire Syst\u00e8mes Complexes et Information Quantique (SCIQ) Lab, ESIEA, 74 bis Avenue Maurice Thorez, 94200 Ivry sur Seine, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"Laboratoire Syst\u00e8mes Complexes et Information Quantique (SCIQ) Lab, ESIEA, 74 bis Avenue Maurice Thorez, 94200 Ivry sur Seine, France","institution_ids":["https://openalex.org/I58581550"]}]},{"author_position":"last","author":{"id":null,"display_name":"Wenjun Zhang","orcid":"https://orcid.org/0000-0002-5990-6670"},"institutions":[{"id":"https://openalex.org/I253932293","display_name":"Anhui University of Traditional Chinese Medicine","ror":"https://ror.org/0139j4p80","country_code":"CN","type":"education","lineage":["https://openalex.org/I253932293"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenjun Zhang","raw_affiliation_strings":["School of Medical Information Engineering, Anhui University of Chinese Medicine, Hefei 230012, China"],"raw_orcid":"https://orcid.org/0000-0002-5990-6670","affiliations":[{"raw_affiliation_string":"School of Medical Information Engineering, Anhui University of Chinese Medicine, Hefei 230012, China","institution_ids":["https://openalex.org/I253932293"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100317994"],"corresponding_institution_ids":["https://openalex.org/I253932293","https://openalex.org/I40963666","https://openalex.org/I58581550"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32230188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"11","first_page":"1155","last_page":"1155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9350000023841858,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9350000023841858,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.008299999870359898,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.00430000014603138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.6753000020980835},{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.6266999840736389},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.5460000038146973},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5051000118255615},{"id":"https://openalex.org/keywords/elementary-cellular-automaton","display_name":"Elementary cellular automaton","score":0.4997999966144562},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49390000104904175},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4722000062465668},{"id":"https://openalex.org/keywords/supervised-learning","display_name":"Supervised learning","score":0.43209999799728394}],"concepts":[{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.6753000020980835},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.6266999840736389},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.611299991607666},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5795999765396118},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.5460000038146973},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5051000118255615},{"id":"https://openalex.org/C193261270","wikidata":"https://www.wikidata.org/wiki/Q1875447","display_name":"Elementary cellular automaton","level":5,"score":0.4997999966144562},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49390000104904175},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4722000062465668},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.43209999799728394},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C120822770","wikidata":"https://www.wikidata.org/wiki/Q5156355","display_name":"Competitive learning","level":3,"score":0.34299999475479126},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32580000162124634},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.29499998688697815},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.29089999198913574},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e27111155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111155","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1155/pdf?version=1763114454","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41294998","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41294998","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:687fd99a92ab4ac89e5b0a5580b5d9ca","is_oa":true,"landing_page_url":"https://doaj.org/article/687fd99a92ab4ac89e5b0a5580b5d9ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 11, p 1155 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27111155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111155","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1155/pdf?version=1763114454","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3172941994","display_name":"\u9057\u5fd8-\u8bb0\u5fc6\u4f20\u64ad\u6a21\u578b\u7684\u590d\u6742\u52a8\u529b\u5b66\u548c\u76f8\u53d8\u7279\u5f81\u7814\u7a76","funder_award_id":"61873104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3676855292","display_name":null,"funder_award_id":"11505071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G455919446","display_name":null,"funder_award_id":"2024YFA1611003","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4777909729","display_name":null,"funder_award_id":"BP0820038","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"},{"id":"https://openalex.org/G7260248977","display_name":null,"funder_award_id":"BP0820038","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321435","display_name":"Anhui University","ror":"https://ror.org/05th6yx34"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416199658.pdf","grobid_xml":"https://content.openalex.org/works/W4416199658.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W73664811","https://openalex.org/W1483113211","https://openalex.org/W1964541705","https://openalex.org/W1969835036","https://openalex.org/W2027154950","https://openalex.org/W2027461913","https://openalex.org/W2036424138","https://openalex.org/W2036919025","https://openalex.org/W2044593527","https://openalex.org/W2048171061","https://openalex.org/W2053757129","https://openalex.org/W2113095412","https://openalex.org/W2143612262","https://openalex.org/W2149679937","https://openalex.org/W2160653514","https://openalex.org/W2337082154","https://openalex.org/W2806252395","https://openalex.org/W2908202417","https://openalex.org/W2921367084","https://openalex.org/W2966501701","https://openalex.org/W2988047746","https://openalex.org/W3028022888","https://openalex.org/W3103370507","https://openalex.org/W3120231758","https://openalex.org/W3160246678","https://openalex.org/W3217314753","https://openalex.org/W4233187303","https://openalex.org/W4291129548","https://openalex.org/W4310212423","https://openalex.org/W4312075150","https://openalex.org/W4320920383","https://openalex.org/W4387452997","https://openalex.org/W4388867355","https://openalex.org/W4391694726","https://openalex.org/W4392455475","https://openalex.org/W4394822512","https://openalex.org/W4400831251","https://openalex.org/W4401252973"],"related_works":[],"abstract_inverted_index":{"The":[0,132],"local":[1],"rules":[2,83,160],"of":[3,25,49,111,140,157],"elementary":[4],"cellular":[5,35],"automata":[6,38],"(ECA)":[7],"with":[8,128,169],"one-dimensional":[9],"three-cell":[10],"neighborhoods":[11],"are":[12,39,193],"represented":[13],"by":[14],"eight-bit":[15],"binary":[16],"numbers":[17],"that":[18,166,192],"encode":[19],"deterministic":[20],"update":[21],"rules.":[22,113,131],"This":[23],"class":[24],"systems":[26],"is":[27],"also":[28],"commonly":[29],"referred":[30],"to":[31,42,62,123,195],"as":[32,184],"the":[33,47,64,101,104,108,125,138],"Wolfram":[34,72,82,130,142,159,182],"automata.":[36,73],"These":[37],"widely":[40],"utilized":[41],"investigate":[43,63],"self-organization":[44],"phenomena":[45],"and":[46,59,67,107,119,151],"dynamics":[48],"complex":[50],"systems.":[51],"In":[52],"this":[53],"work,":[54],"we":[55,115],"employ":[56],"numerical":[57],"simulations":[58],"computational":[60],"methods":[61,122,135,146,175],"asymptotic":[65,105],"density":[66,106,110,171],"dynamical":[68],"evolution":[69],"mechanisms":[70],"in":[71,179],"We":[74],"explore":[75],"alternative":[76],"initial":[77,109],"conditions":[78],"under":[79],"which":[80],"certain":[81],"generate":[84],"similar":[85,190],"fractal":[86],"patterns":[87],"over":[88],"time,":[89],"even":[90],"when":[91],"starting":[92],"from":[93],"a":[94],"single":[95],"active":[96],"site.":[97],"Our":[98],"results":[99,165],"reveal":[100],"relationship":[102],"between":[103],"selected":[112],"Furthermore,":[114],"apply":[116],"both":[117],"supervised":[118,133],"unsupervised":[120,145],"learning":[121,134,174],"identify":[124,137],"configurations":[126,139,156,191],"associated":[127],"different":[129,158,181],"effectively":[136,187],"various":[141],"rules,":[143,183],"while":[144],"like":[147],"principal":[148],"component":[149],"analysis":[150],"autoencoders":[152],"can":[153,186],"approximately":[154],"cluster":[155],"into":[161],"distinct":[162],"groups,":[163],"yielding":[164],"align":[167],"well":[168],"simulated":[170],"outputs.":[172],"Machine":[173],"offer":[176],"significant":[177],"advantages":[178],"identifying":[180],"they":[185],"distinguish":[188],"highly":[189],"challenging":[194],"differentiate":[196],"manually.":[197]},"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-11-14T00:00:00"}