{"id":"https://openalex.org/W7171678377","doi":"https://doi.org/10.48550/arxiv.2607.24949","title":"A Hybrid Physics-Informed Neural Network Framework for Subcritical and Supercritical Dynamics in Multi-Species Chemotaxis","display_name":"A Hybrid Physics-Informed Neural Network Framework for Subcritical and Supercritical Dynamics in Multi-Species Chemotaxis","publication_year":2026,"publication_date":"2026-07-27","ids":{"openalex":"https://openalex.org/W7171678377","doi":"https://doi.org/10.48550/arxiv.2607.24949"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2607.24949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.24949","pdf_url":"https://arxiv.org/pdf/2607.24949","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2607.24949","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007515296","display_name":"Hamid El Bahja","orcid":"https://orcid.org/0000-0002-0945-2105","observed_orcids":["https://orcid.org/0000-0002-0945-2105"]},"institutions":[{"id":"https://openalex.org/I4405261291","display_name":"AIMS Research and Innovation Centre","ror":"https://ror.org/052gr0y82","country_code":"RW","type":"education","lineage":["https://openalex.org/I4405261291"]}],"countries":["RW"],"is_corresponding":false,"raw_author_name":"Bahja, Hamid El","raw_affiliation_strings":["African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany","institution_ids":["https://openalex.org/I4405261291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5143914783","display_name":"Jan C. Riedel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]},{"id":"https://openalex.org/I4405261291","display_name":"AIMS Research and Innovation Centre","ror":"https://ror.org/052gr0y82","country_code":"RW","type":"education","lineage":["https://openalex.org/I4405261291"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE","RW"],"is_corresponding":false,"raw_author_name":"Riedel, Jan C.","raw_affiliation_strings":["African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany","Technical University Berlin & German Aerospace Center (DLR) , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany","institution_ids":["https://openalex.org/I4405261291"]},{"raw_affiliation_string":"Technical University Berlin & German Aerospace Center (DLR) , Germany","institution_ids":["https://openalex.org/I2898391981","https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5143913126","display_name":"Peter Jung","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405261291","display_name":"AIMS Research and Innovation Centre","ror":"https://ror.org/052gr0y82","country_code":"RW","type":"education","lineage":["https://openalex.org/I4405261291"]}],"countries":["RW"],"is_corresponding":false,"raw_author_name":"Jung, Peter","raw_affiliation_strings":["African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"African Institute for Mathematical Sciences , Research and Innovation Centre , Kigali , Rwanda Technical University Berlin , Germany","institution_ids":["https://openalex.org/I4405261291"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9940999746322632,"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":0.9940999746322632,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.00430000014603138,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10320","display_name":"Neural Networks and Applications","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.871999979019165},{"id":"https://openalex.org/keywords/finite-time-blow-up","display_name":"finite-time blow-up","score":0.9860000014305115},{"id":"https://openalex.org/keywords/aggregation","display_name":"aggregation","score":0.5830000042915344},{"id":"https://openalex.org/keywords/backward-euler-time-stepping","display_name":"backward Euler time-stepping","score":0.8209999799728394},{"id":"https://openalex.org/keywords/logarithmic-transformation","display_name":"logarithmic transformation","score":0.7929999828338623}],"concepts":[{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.7064999938011169},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.46880000829696655},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.4253000020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40369999408721924},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.390500009059906},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37220001220703125},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.35839998722076416},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3228999972343445},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2912999987602234},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.26089999079704285}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.24949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.24949","pdf_url":"https://arxiv.org/pdf/2607.24949","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2607.24949","doi":"https://doi.org/10.48550/arxiv.2607.24949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.24949","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,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2607.24949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.24949","pdf_url":"https://arxiv.org/pdf/2607.24949","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7171678377.pdf","grobid_xml":"https://content.openalex.org/works/W7171678377.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4411532207","https://openalex.org/W4225497254","https://openalex.org/W4220869134","https://openalex.org/W7109156859","https://openalex.org/W7222559961","https://openalex.org/W7197014024","https://openalex.org/W4381852607","https://openalex.org/W7208815106","https://openalex.org/W7106162689","https://openalex.org/W4415673080"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,37,89,100,109,129,143],"two-species":[3],"chemotaxis":[4],"system":[5],"that":[6,53,113,155],"exhibits":[7],"two":[8],"qualitatively":[9],"different":[10],"regimes:":[11],"subcritical":[12,33,161],"dynamics,":[13,21,162],"in":[14,22,174],"which":[15,23],"solutions":[16],"remain":[17],"smooth,":[18,139],"and":[19,51,57,77,108,131,171],"supercritical":[20,62,176],"strong":[24],"aggregation":[25,170],"may":[26],"lead":[27],"to":[28,71,103,127,142],"finite-time":[29,172],"blow-up.":[30,82],"In":[31,60],"the":[32,48,61,73,136,156,164,175],"regime,":[34,63],"we":[35,87],"use":[36,128],"standard":[38],"continuous-time":[39,157],"physics-informed":[40],"neural":[41],"network":[42],"(PINN)":[43],"with":[44,81,99],"alternating":[45],"training":[46,115],"for":[47],"coupled":[49],"fields":[50],"show":[52],"it":[54],"provides":[55],"accurate":[56],"efficient":[58],"approximations.":[59],"however,":[64],"this":[65,85],"formulation":[66,147,158,166],"is":[67,138],"not":[68],"sufficiently":[69],"robust":[70,145],"resolve":[72],"highly":[74],"localized":[75],"structures":[76],"steep":[78],"gradients":[79],"associated":[80],"To":[83],"address":[84],"limitation,":[86],"introduce":[88],"discrete-time":[90,165],"PINN":[91,134],"based":[92],"on":[93],"backward":[94],"Euler":[95],"time":[96],"stepping,":[97],"combined":[98],"logarithmic":[101],"transformation":[102],"stabilize":[104],"large":[105],"solution":[106,137],"values":[107],"residual-adaptive":[110],"collocation":[111],"strategy":[112],"concentrates":[114],"points":[116],"near":[117],"regions":[118],"of":[119],"high":[120],"activity.":[121],"This":[122],"hybrid":[123],"framework":[124],"allows":[125],"us":[126],"simple":[130],"computationally":[132],"inexpensive":[133],"when":[135,148],"while":[140,163],"switching":[141],"more":[144],"discrete":[146],"singular":[149,169],"dynamics":[150],"emerge.":[151],"Numerical":[152],"experiments":[153],"confirm":[154],"accurately":[159],"resolves":[160],"reliably":[167],"captures":[168],"blow-up":[173],"regime.":[177]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-07-30T00:00:00"}