{"id":"https://openalex.org/W7133337743","doi":"https://doi.org/10.48550/arxiv.2603.00397","title":"TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions","display_name":"TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions","publication_year":2026,"publication_date":"2026-02-28","ids":{"openalex":"https://openalex.org/W7133337743","doi":"https://doi.org/10.48550/arxiv.2603.00397"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00397","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00397","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.00397","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127935138","display_name":"Hongjie Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jiang, Hongjie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127904090","display_name":"Di Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Di","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5127935138"],"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":0.9879000186920166,"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":0.9879000186920166,"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/T11416","display_name":"Numerical methods for differential equations","score":0.002300000051036477,"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"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0017999999690800905,"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/solver","display_name":"Solver","score":0.6938999891281128},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6431000232696533},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6079999804496765},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5899999737739563},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.586899995803833},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5386999845504761},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.3296000063419342}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6938999891281128},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6431000232696533},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6079999804496765},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5899999737739563},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.586899995803833},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5386999845504761},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5249000191688538},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5091000199317932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42309999465942383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3953999876976013},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3296000063419342},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31779998540878296},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2987000048160553},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00397","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00397","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.00397","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00397","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Accurately":[0],"solving":[1],"time-dependent":[2],"partial":[3],"differential":[4],"equations":[5],"(PDEs)":[6],"with":[7,96],"neural":[8,30,113],"networks":[9],"remains":[10],"challenging":[11],"due":[12],"to":[13,40],"long-time":[14],"error":[15],"accumulation":[16],"and":[17,60,67,93,111],"the":[18,35],"difficulty":[19],"of":[20],"enforcing":[21],"general":[22,43],"boundary":[23,44,61,98],"conditions.":[24],"We":[25],"introduce":[26],"TENG-BC,":[27],"a":[28,52,71,77],"high-precision":[29],"PDE":[31],"solver":[32],"based":[33],"on":[34],"Time-Evolving":[36],"Natural":[37],"Gradient,":[38],"designed":[39],"perform":[41],"under":[42,104],"constraints.":[45],"At":[46],"each":[47],"time":[48,82],"step,":[49],"TENG-BC":[50,100],"performs":[51],"boundary-aware":[53],"optimization":[54],"that":[55],"jointly":[56],"enforces":[57],"interior":[58],"dynamics":[59],"conditions,":[62,99],"accommodating":[63],"Dirichlet,":[64],"Neumann,":[65],"Robin,":[66],"mixed":[68],"types":[69],"within":[70],"unified":[72],"framework.":[73],"This":[74],"formulation":[75],"admits":[76],"natural-gradient":[78],"interpretation,":[79],"enabling":[80],"stable":[81],"evolution":[83],"without":[84],"delicate":[85],"penalty":[86],"tuning.":[87],"Across":[88],"benchmarks":[89],"over":[90],"diffusion,":[91],"transport,":[92],"nonlinear":[94],"PDEs":[95],"various":[97],"achieves":[101],"solver-level":[102],"accuracy":[103],"comparable":[105],"sampling":[106],"budgets,":[107],"outperforming":[108],"conventional":[109],"solvers":[110],"physics-informed":[112],"network":[114],"(PINN)":[115],"baselines.":[116]},"counts_by_year":[],"updated_date":"2026-03-04T07:09:34.246503","created_date":"2026-03-04T00:00:00"}
