{"id":"https://openalex.org/W7214714594","doi":"https://doi.org/10.48550/arxiv.2609.31955","title":"From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws","display_name":"From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214714594","doi":"https://doi.org/10.48550/arxiv.2609.31955"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31955","pdf_url":"https://arxiv.org/pdf/2609.31955","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/2609.31955","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084148497","display_name":"Rainey Lyons","orcid":"https://orcid.org/0000-0003-4113-0357","observed_orcids":["https://orcid.org/0000-0003-4113-0357"]},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lyons, Rainey","raw_affiliation_strings":["Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056970932","display_name":"Vanja Duki\u0107","orcid":"https://orcid.org/0000-0002-0348-0834","observed_orcids":["https://orcid.org/0000-0002-0348-0834"]},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dukic, Vanja","raw_affiliation_strings":["Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089222534","display_name":"David M. Bortz","orcid":"https://orcid.org/0000-0003-1163-7317","observed_orcids":["https://orcid.org/0000-0003-1163-7317"]},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bortz, David M","raw_affiliation_strings":["Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Colorado , Boulder CO 80309-0526 , USA","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.7670999765396118,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.7670999765396118,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12859","display_name":"Cell Image Analysis Techniques","score":0.09570000320672989,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.03869999945163727,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cell-to-cell-variability","display_name":"cell-to-cell variability","score":0.699999988079071},{"id":"https://openalex.org/keywords/nonlinear-dynamics","display_name":"nonlinear dynamics","score":0.7710000276565552},{"id":"https://openalex.org/keywords/empirical-bayes-shrinkage","display_name":"empirical Bayes shrinkage","score":0.9509999752044678},{"id":"https://openalex.org/keywords/random-effects-model","display_name":"random effects models","score":0.8939999938011169},{"id":"https://openalex.org/keywords/parameter-heterogeneity","display_name":"parameter heterogeneity","score":0.7369999885559082},{"id":"https://openalex.org/keywords/population-density","display_name":"population density","score":0.5590000152587891}],"concepts":[{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.5383999943733215},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4643000066280365},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.46389999985694885},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.41440001130104065},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.38429999351501465},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3840000033378601},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37290000915527344},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3716999888420105},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C169733012","wikidata":"https://www.wikidata.org/wiki/Q1613416","display_name":"Population size","level":3,"score":0.36640000343322754},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.33970001339912415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33230000734329224},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C77352025","wikidata":"https://www.wikidata.org/wiki/Q386191","display_name":"Population growth","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31955","pdf_url":"https://arxiv.org/pdf/2609.31955","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.2609.31955","doi":"https://doi.org/10.48550/arxiv.2609.31955","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31955","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:2609.31955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31955","pdf_url":"https://arxiv.org/pdf/2609.31955","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":[{"id":"https://openalex.org/G1322734375","display_name":null,"funder_award_id":"20196701429919","funder_id":"https://openalex.org/F4320332299","funder_display_name":"National Institute of Food and Agriculture"},{"id":"https://openalex.org/G1522534585","display_name":null,"funder_award_id":"2109774","funder_id":"https://openalex.org/F4320337400","funder_display_name":"Division of Environmental Biology"},{"id":"https://openalex.org/G4981355530","display_name":null,"funder_award_id":"2054085","funder_id":"https://openalex.org/F4320332167","funder_display_name":"Directorate for Biological Sciences"},{"id":"https://openalex.org/G5589623480","display_name":null,"funder_award_id":"DEB-2109774","funder_id":"https://openalex.org/F4320337400","funder_display_name":"Division of Environmental Biology"},{"id":"https://openalex.org/G5771670750","display_name":null,"funder_award_id":"2054085","funder_id":"https://openalex.org/F4320337397","funder_display_name":"Division of Molecular and Cellular Biosciences"},{"id":"https://openalex.org/G9000889326","display_name":"Data-driven and science-informed methods for the discovery of biomedical mechanisms and processes","funder_award_id":"R35GM149335","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320332167","display_name":"Directorate for Biological Sciences","ror":"https://ror.org/001xhss06"},{"id":"https://openalex.org/F4320332299","display_name":"National Institute of Food and Agriculture","ror":"https://ror.org/05qx3fv49"},{"id":"https://openalex.org/F4320332538","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"},{"id":"https://openalex.org/F4320337397","display_name":"Division of Molecular and Cellular Biosciences","ror":"https://ror.org/002jdaq33"},{"id":"https://openalex.org/F4320337400","display_name":"Division of Environmental Biology","ror":"https://ror.org/03g87he71"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214714594.pdf","grobid_xml":"https://content.openalex.org/works/W7214714594.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2586808014","https://openalex.org/W4417116585","https://openalex.org/W3198054947","https://openalex.org/W2467600229","https://openalex.org/W3133020697","https://openalex.org/W2121904595","https://openalex.org/W3024936547","https://openalex.org/W2952154064","https://openalex.org/W3178178192","https://openalex.org/W2559508236"],"abstract_inverted_index":{"Single-cell":[0],"time-lapse":[1],"microscopy":[2],"now":[3],"provides":[4],"high-resolution":[5],"size":[6,86,96],"trajectories":[7],"for":[8,16],"thousands":[9],"of":[10,22,28,45,61],"individual":[11,85],"cells,":[12],"yet":[13],"principled":[14],"methods":[15],"simultaneously":[17],"learning":[18],"the":[19,26,41,53,80,100,122,126,133],"functional":[20],"form":[21],"growth":[23,56,68,91],"laws":[24,92],"and":[25,64,93,107],"distribution":[27],"cell-to-cell":[29],"physiological":[30],"variability":[31],"remain":[32],"limited.":[33],"We":[34,78,114],"present":[35],"a":[36,59,75,118],"data-driven":[37],"framework":[38],"based":[39],"on":[40,82,120],"recent":[42],"Weak-form":[43],"Estimation":[44],"Nonlinear":[46],"Dynamics":[47],"(WENDy)":[48],"algorithm":[49],"to":[50,132],"(i)":[51],"select":[52],"best":[54],"supported":[55],"law":[57],"from":[58],"set":[60],"candidate":[62],"laws,":[63],"(ii)":[65],"recover":[66],"individual-level":[67],"parameters":[69],"via":[70],"empirical":[71],"Bayes":[72],"shrinkage":[73],"within":[74],"random-effects":[76],"model.":[77],"demonstrate":[79],"approach":[81],"both":[83,104],"synthetic":[84],"data":[87],"incorporating":[88],"commonly":[89],"found":[90],"recorded":[94],"real":[95],"trajectories,":[97],"showing":[98],"that":[99],"method":[101,127],"accurately":[102],"recovers":[103],"growth-law":[105],"structure":[106],"parameter":[108],"heterogeneity":[109],"at":[110],"reasonable":[111],"noise":[112],"levels.":[113],"finally":[115],"end":[116],"with":[117],"discussion":[119],"how":[121],"results":[123],"obtained":[124],"by":[125],"here":[128],"can":[129],"be":[130],"upscaled":[131],"population":[134],"level.":[135]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-30T00:00:00"}
