{"id":"https://openalex.org/W7204878076","doi":"https://doi.org/10.48550/arxiv.2608.28870","title":"Physics-Informed Basis Functions for Nonlinear Response Curve Decomposition: A Parsimonious Alternative to Splines","display_name":"Physics-Informed Basis Functions for Nonlinear Response Curve Decomposition: A Parsimonious Alternative to Splines","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204878076","doi":"https://doi.org/10.48550/arxiv.2608.28870"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28870","pdf_url":"https://arxiv.org/pdf/2608.28870","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28870","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002864766","display_name":"M. Ross Kunz","orcid":"https://orcid.org/0000-0001-8878-8274","observed_orcids":["https://orcid.org/0000-0001-8878-8274"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kunz, M. Ross","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148840868","display_name":"Jieun Lee","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Jieun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5114128108","display_name":"Jaden Palmer","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Palmer, Jaden","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":0.2572999894618988,"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":0.2572999894618988,"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/T11236","display_name":"Control Systems and Identification","score":0.2549000084400177,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.09950000047683716,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-decay","display_name":"exponential decay","score":0.9890000224113464},{"id":"https://openalex.org/keywords/curve-fitting","display_name":"curve fitting","score":0.5580000281333923},{"id":"https://openalex.org/keywords/interpretable-models","display_name":"interpretable models","score":0.5059999823570251},{"id":"https://openalex.org/keywords/solutions-of-differential-equations","display_name":"solutions of differential equations","score":0.5440000295639038}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894999742507935},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6241000294685364},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5803999900817871},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.54830002784729},{"id":"https://openalex.org/C151620405","wikidata":"https://www.wikidata.org/wiki/Q826116","display_name":"Log-normal distribution","level":2,"score":0.5473999977111816},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5220999717712402},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49230000376701355},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.49149999022483826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47200000286102295},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.4309999942779541},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3727000057697296},{"id":"https://openalex.org/C46889948","wikidata":"https://www.wikidata.org/wiki/Q2755024","display_name":"Nonlinear regression","level":3,"score":0.3416000008583069},{"id":"https://openalex.org/C199435849","wikidata":"https://www.wikidata.org/wiki/Q3179293","display_name":"Shape parameter","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.33149999380111694},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.2906999886035919},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C149810388","wikidata":"https://www.wikidata.org/wiki/Q5374873","display_name":"Emulation","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2752000093460083},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C2776913854","wikidata":"https://www.wikidata.org/wiki/Q25345887","display_name":"Growth curve (statistics)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.262800008058548}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28870","pdf_url":"https://arxiv.org/pdf/2608.28870","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.2608.28870","doi":"https://doi.org/10.48550/arxiv.2608.28870","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28870","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28870","pdf_url":"https://arxiv.org/pdf/2608.28870","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1969590420","https://openalex.org/W2979838186","https://openalex.org/W2312902148","https://openalex.org/W1484997996","https://openalex.org/W2291228929","https://openalex.org/W2886736785","https://openalex.org/W3210841842","https://openalex.org/W563762431","https://openalex.org/W1585339076","https://openalex.org/W2796638121"],"abstract_inverted_index":{"Curve":[0,29],"fitting":[1],"for":[2],"physical,":[3,88],"biological,":[4,89],"and":[5,18,45,63,69,85,90,107,115],"engineering":[6],"data":[7],"typically":[8],"forces":[9],"a":[10,31,39,53],"choice":[11],"between":[12],"interpretable":[13],"but":[14,20],"rigid":[15],"parametric":[16],"forms":[17],"flexible":[19],"physically":[21,116],"opaque":[22],"smoothers.":[23],"This":[24],"paper":[25],"introduces":[26],"the":[27,36,74,78,95],"Growth-Decay":[28],"(GDC),":[30],"physics-informed":[32],"basis":[33,104],"derived":[34],"as":[35],"product":[37],"of":[38,98],"lognormal":[40],"growth":[41,62],"cumulative":[42],"distribution":[43],"function":[44,105],"an":[46],"exponential":[47],"decay":[48,64],"term,":[49],"each":[50],"traceable":[51],"to":[52,61,77],"governing":[54],"differential":[55],"equation.":[56],"GDC's":[57],"parameters":[58],"correspond":[59],"directly":[60],"timescales,":[65],"yielding":[66],"dimensionless":[67],"ratios":[68],"shape":[70],"descriptors":[71],"that":[72],"connect":[73],"fit":[75,96],"back":[76],"underlying":[79],"dynamics.":[80],"Across":[81],"simulated":[82],"differential-equation":[83],"solutions":[84],"applications":[86],"spanning":[87],"economic":[91],"data,":[92],"GDC":[93],"matches":[94],"quality":[97],"splines,":[99],"generalized":[100],"additive":[101],"models,":[102],"radial":[103],"networks,":[106],"Fourier":[108],"regression,":[109],"while":[110],"remaining":[111],"substantially":[112],"more":[113],"parsimonious":[114],"interpretable.":[117]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-02T00:00:00"}
