{"id":"https://openalex.org/W7156880605","doi":"https://doi.org/10.48550/arxiv.2604.23003","title":"Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen","display_name":"Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen","publication_year":2026,"publication_date":"2026-04-24","ids":{"openalex":"https://openalex.org/W7156880605","doi":"https://doi.org/10.48550/arxiv.2604.23003"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.23003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23003","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":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.2604.23003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020732029","display_name":"Leszek Siwik","orcid":"https://orcid.org/0000-0003-0535-7220"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siwik, Leszek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113270067","display_name":"Maciej Sikora","orcid":"https://orcid.org/0009-0006-4465-2395"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sikora, Maciej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134789610","display_name":"Natalia Leszczy\u0144ska","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leszczy\u0144ska, Natalia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114367846","display_name":"Tomasz Maciej Ciesielski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ciesielski, Tomasz Maciej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051867074","display_name":"Eirik Valseth","orcid":"https://orcid.org/0000-0001-6940-4191"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Valseth, Eirik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040211348","display_name":"Manuela Bastidas Olivares","orcid":"https://orcid.org/0000-0002-3006-2363"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivares, Manuela Bastidas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126590126","display_name":"Marcin \u0141o\u015b","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0141o\u015b, Marcin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134779991","display_name":"Tomasz S\u0142u\u017calec","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S\u0142u\u017calec, Tomasz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101960746","display_name":"Jacek Leszczy\u0144ski","orcid":"https://orcid.org/0000-0002-4927-1472"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leszczy\u0144ski, Jacek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126632386","display_name":"Maciej Paszy\u0144ski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paszy\u0144ski, Maciej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":10,"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/T12120","display_name":"Air Quality Monitoring and Forecasting","score":0.5716999769210815,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12120","display_name":"Air Quality Monitoring and Forecasting","score":0.5716999769210815,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.048700001090765,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.03759999945759773,"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/inversion","display_name":"Inversion (geology)","score":0.7670000195503235},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.736299991607666},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.5457000136375427},{"id":"https://openalex.org/keywords/pollution","display_name":"Pollution","score":0.421099990606308},{"id":"https://openalex.org/keywords/backpropagation","display_name":"Backpropagation","score":0.3937000036239624},{"id":"https://openalex.org/keywords/air-pollution","display_name":"Air pollution","score":0.38280001282691956},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3644999861717224},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.35910001397132874}],"concepts":[{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.7670000195503235},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.736299991607666},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.5457000136375427},{"id":"https://openalex.org/C521259446","wikidata":"https://www.wikidata.org/wiki/Q58734","display_name":"Pollution","level":2,"score":0.421099990606308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4075999855995178},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.3937000036239624},{"id":"https://openalex.org/C559116025","wikidata":"https://www.wikidata.org/wiki/Q131123","display_name":"Air pollution","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C24245907","wikidata":"https://www.wikidata.org/wiki/Q498957","display_name":"Particulates","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32280001044273376},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.2937999963760376},{"id":"https://openalex.org/C118365302","wikidata":"https://www.wikidata.org/wiki/Q4817115","display_name":"Atmospheric model","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.28929999470710754},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27129998803138733},{"id":"https://openalex.org/C82685317","wikidata":"https://www.wikidata.org/wiki/Q19829510","display_name":"Pollutant","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C126314574","wikidata":"https://www.wikidata.org/wiki/Q2364111","display_name":"Air quality index","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2574999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.23003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23003","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.23003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23003","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":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":{"In":[0],"this":[1,47],"paper,":[2],"we":[3,50,95],"propose":[4],"a":[5,23,52,80,92],"Physics-Informed":[6],"Neural":[7],"Network":[8],"framework":[9,26,117],"for":[10,27],"time-dependent":[11,29],"simulations":[12],"of":[13,39,124],"pollution":[14,97],"propagation":[15,98],"originating":[16],"from":[17],"moving":[18],"emission":[19],"sources.":[20],"We":[21],"formulate":[22],"robust":[24,53],"variational":[25],"the":[28,34,40,61,67,70,75,122,143],"advection-diffusion":[30],"problem":[31],"and":[32,36,74,138,151],"establish":[33],"boundedness":[35],"inf-sup":[37],"stability":[38],"corresponding":[41],"discrete":[42],"weak":[43],"formulation.":[44],"Based":[45],"on":[46,127],"mathematical":[48],"foundation,":[49],"construct":[51],"loss":[54],"function":[55],"that":[56,133],"is":[57,83,118],"directly":[58],"related":[59],"to":[60,85,120],"true":[62],"approximation":[63,73],"error,":[64],"defined":[65],"as":[66],"difference":[68],"between":[69],"neural":[71,88],"network":[72,89],"(unknown)":[76],"exact":[77],"solution.":[78],"Additionally,":[79],"collocation-based":[81],"strategy":[82],"introduced":[84],"speed":[86],"up":[87],"training.":[90],"As":[91],"case":[93],"study,":[94],"investigate":[96],"caused":[99],"by":[100,107],"snowmobile":[101],"traffic":[102],"in":[103],"Longyearbyen,":[104],"Spitsbergen,":[105],"supported":[106],"detailed":[108],"in-field":[109],"measurements":[110],"collected":[111],"using":[112],"dedicated":[113],"sensors.":[114],"The":[115],"proposed":[116],"applied":[119],"analyze":[121],"effects":[123],"thermal":[125,134],"inversion":[126,135],"pollutant":[128],"accumulation.":[129],"Our":[130],"results":[131],"demonstrate":[132],"traps":[136],"dense":[137],"humid":[139],"air":[140,154],"masses":[141],"near":[142],"ground,":[144],"significantly":[145],"enhancing":[146],"particulate":[147],"matter":[148],"(PM)":[149],"concentration":[150],"worsening":[152],"local":[153],"quality.":[155]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-29T00:00:00"}
