{"id":"https://openalex.org/W7140837204","doi":"https://doi.org/10.48550/arxiv.2603.23977","title":"Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception","display_name":"Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140837204","doi":"https://doi.org/10.48550/arxiv.2603.23977"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23977","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23977","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.2603.23977","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127394509","display_name":"Tongfei Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Tongfei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130678867","display_name":"Jingying Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Jingying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130703298","display_name":"Linlin Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Linlin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130685127","display_name":"Juan Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Juan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124750825","display_name":"Jinhu L\u00fc","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L\u00fc, Jinhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Doermann, David","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Doermann, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127482482","display_name":"Chunyu Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Chunyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"He, Long","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Long","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130642183","display_name":"Tian Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Tian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127823427","display_name":"Guodong Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Guodong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130694287","display_name":"Baochang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Baochang","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":0.5934000015258789,"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":0.5934000015258789,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.21389999985694885,"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"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.06769999861717224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5519000291824341},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5212000012397766},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.5175999999046326},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.5102999806404114},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.4368000030517578},{"id":"https://openalex.org/keywords/perception","display_name":"Perception","score":0.4332999885082245},{"id":"https://openalex.org/keywords/sensory-system","display_name":"Sensory system","score":0.3806000053882599},{"id":"https://openalex.org/keywords/network-architecture","display_name":"Network architecture","score":0.34599998593330383}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7156000137329102},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6474999785423279},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5519000291824341},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5212000012397766},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5175999999046326},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.4368000030517578},{"id":"https://openalex.org/C26760741","wikidata":"https://www.wikidata.org/wiki/Q160402","display_name":"Perception","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C94487597","wikidata":"https://www.wikidata.org/wiki/Q11101","display_name":"Sensory system","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.36570000648498535},{"id":"https://openalex.org/C193415008","wikidata":"https://www.wikidata.org/wiki/Q639681","display_name":"Network architecture","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C2780186347","wikidata":"https://www.wikidata.org/wiki/Q11414","display_name":"Subnetwork","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C28063669","wikidata":"https://www.wikidata.org/wiki/Q7167042","display_name":"Perceptual system","level":3,"score":0.2985000014305115},{"id":"https://openalex.org/C2983568541","wikidata":"https://www.wikidata.org/wiki/Q389772","display_name":"Information transmission","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.25099998712539673},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23977","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23977","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.2603.23977","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23977","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/16","display_name":"Peace, Justice and strong institutions","score":0.4185900390148163}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Deep":[0],"networks":[1],"often":[2],"rely":[3],"on":[4,107],"architectural":[5],"heuristics":[6],"to":[7,14],"shape":[8],"representation":[9,34,128],"evolution,":[10],"limiting":[11],"their":[12],"ability":[13],"model":[15],"data":[16],"governed":[17],"by":[18],"intrinsic":[19],"dynamics.":[20],"We":[21],"present":[22],"the":[23],"Circuit-inspired":[24],"High-Order":[25],"Neural":[26,53],"Network":[27],"(CHONN),":[28],"a":[29,37,56,137],"modular":[30],"framework":[31],"that":[32,86,97],"treats":[33],"evolution":[35],"as":[36,136],"latent":[38],"potential":[39],"process":[40],"and":[41,77,93,117,126],"increases":[42],"its":[43],"effective":[44],"order":[45],"through":[46],"Kirchhoff-inspired":[47],"cascade":[48],"composition.":[49],"A":[50],"single":[51],"Kirchhoff":[52],"Cell":[54],"implements":[55],"stable":[57,76],"first-order":[58],"update,":[59],"while":[60],"serially":[61],"composed":[62],"cells":[63,88],"form":[64],"higher-order":[65],"dynamical":[66],"operators":[67],"within":[68],"one":[69],"block.":[70],"This":[71],"construction":[72,100],"is":[73],"interpretable,":[74],"numerically":[75],"compatible":[78],"with":[79],"common":[80],"neural":[81,141],"backbones.":[82],"Theoretical":[83],"analysis":[84],"shows":[85],"cascaded":[87],"induce":[89],"end-to-end":[90],"high-order":[91,99,133],"operators,":[92],"controlled":[94],"experiments":[95],"demonstrate":[96],"intra-block":[98],"differs":[101],"from":[102],"generic":[103],"depth":[104],"stacking,":[105],"especially":[106],"derivative-sensitive":[108],"measures.":[109],"Across":[110],"steady-state":[111],"operator":[112],"learning,":[113],"long-horizon":[114],"physical":[115],"forecasting":[116],"ImageNet-1K":[118],"recognition,":[119],"CHONN":[120],"improves":[121],"structural":[122],"fidelity,":[123],"rollout":[124],"stability":[125],"visual":[127],"learning.":[129],"These":[130],"results":[131],"identify":[132],"circuit":[134],"composition":[135],"general":[138],"principle":[139],"for":[140],"dynamics":[142],"modeling.":[143]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-27T00:00:00"}