{"id":"https://openalex.org/W7126158508","doi":"https://doi.org/10.48550/arxiv.2601.20978","title":"Solution of Advection Equation with Discontinuous Initial and Boundary Conditions via Physics-Informed Neural Networks","display_name":"Solution of Advection Equation with Discontinuous Initial and Boundary Conditions via Physics-Informed Neural Networks","publication_year":2026,"publication_date":"2026-01-28","ids":{"openalex":"https://openalex.org/W7126158508","doi":"https://doi.org/10.48550/arxiv.2601.20978"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2601.20978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124383967","display_name":"Omid Khosravi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khosravi, Omid","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068934056","display_name":"Mehdi Tatari","orcid":"https://orcid.org/0000-0002-3080-964X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tatari, Mehdi","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":0.9943000078201294,"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":0.9943000078201294,"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":0.0010000000474974513,"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":0.00039999998989515007,"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/smoothing","display_name":"Smoothing","score":0.6820999979972839},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6565999984741211},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.59579998254776},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.504800021648407},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4973999857902527},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4722999930381775},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4392000138759613},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41440001130104065},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41339999437332153}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6820999979972839},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6565999984741211},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.59579998254776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5507000088691711},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4973999857902527},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46779999136924744},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3734000027179718},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.34470000863075256},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32249999046325684},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C140101238","wikidata":"https://www.wikidata.org/wiki/Q1404885","display_name":"Window function","level":3,"score":0.30160000920295715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29910001158714294},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C137685913","wikidata":"https://www.wikidata.org/wiki/Q4316763","display_name":"Nonlinear filter","level":4,"score":0.27379998564720154},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2601.20978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2601.20978","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.20978","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":"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":"pmh:doi:10.48550/arxiv.2601.20978","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,36,102],"investigate":[4],"several":[5],"techniques":[6],"for":[7,13,98],"modeling":[8],"the":[9,32,44,54,59,74,83,87,110,116],"one-dimensional":[10],"advection":[11],"equation":[12],"a":[14,38,48,77,93,104],"specific":[15],"class":[16],"of":[17,119],"problems":[18],"with":[19],"discontinuous":[20,120],"initial":[21],"and":[22,58,66,86],"boundary":[23],"conditions":[24],"using":[25],"physics-informed":[26],"neural":[27,60,125],"networks":[28],"(PINNs).":[29],"To":[30,71],"mitigate":[31],"spectral":[33],"bias":[34],"phenomenon,":[35],"employ":[37],"Fourier":[39,55],"feature":[40,56],"mapping":[41],"layer":[42],"as":[43],"input":[45],"representation,":[46],"adopt":[47],"two-stage":[49],"training":[50],"strategy":[51],"in":[52,124],"which":[53],"parameters":[57],"network":[61,126],"weights":[62],"are":[63],"optimized":[64],"sequentially,":[65],"incorporate":[67],"adaptive":[68],"loss":[69,106],"weighting.":[70],"further":[72],"enhance":[73],"approximation":[75],"accuracy,":[76],"median":[78],"filter":[79],"is":[80,90],"applied":[81],"to":[82,114],"spatial":[84],"data,":[85],"predicted":[88],"solution":[89],"constrained":[91],"through":[92],"bounded":[94],"linear":[95],"mapping.":[96],"Moreover,":[97],"certain":[99],"nonlinear":[100],"problems,":[101],"introduce":[103],"modified":[105],"function":[107],"inspired":[108],"by":[109],"upwind":[111],"numerical":[112],"scheme":[113],"alleviate":[115],"excessive":[117],"smoothing":[118],"solutions":[121],"typically":[122],"observed":[123],"approximations.":[127]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-01T00:00:00"}
