{"id":"https://openalex.org/W7214930212","doi":"https://doi.org/10.48550/arxiv.2609.37083","title":"Identifying ODEs from Unstructured Data with Causal Representation Learning","display_name":"Identifying ODEs from Unstructured Data with Causal Representation Learning","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214930212","doi":"https://doi.org/10.48550/arxiv.2609.37083"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37083","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37083","pdf_url":"https://arxiv.org/pdf/2609.37083","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/2609.37083","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124779661","display_name":"Alessandro Trenta","orcid":"https://orcid.org/0009-0007-9188-5666","observed_orcids":["https://orcid.org/0009-0007-9188-5666"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Trenta, Alessandro","raw_affiliation_strings":["Department of Computer Science University of Pisa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Pisa","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068371154","display_name":"Riccardo Massidda","orcid":"https://orcid.org/0000-0003-0137-7793","observed_orcids":["https://orcid.org/0000-0003-0137-7793"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massidda, Riccardo","raw_affiliation_strings":["Department of Computer Science University of Pisa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Pisa","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053890378","display_name":"Davide Bacciu","orcid":"https://orcid.org/0000-0001-5213-2468","observed_orcids":["https://orcid.org/0000-0001-5213-2468"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bacciu, Davide","raw_affiliation_strings":["Department of Computer Science University of Pisa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Pisa","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073301822","display_name":"Sara Magliacane","orcid":"https://orcid.org/0000-0002-1360-2639","observed_orcids":["https://orcid.org/0000-0002-1360-2639"]},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE","NL"],"is_corresponding":false,"raw_author_name":"Magliacane, Sara","raw_affiliation_strings":["Saarland Informatics Campus Saarland University & University of Amsterdam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus Saarland University & University of Amsterdam","institution_ids":["https://openalex.org/I887064364","https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":3,"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":0.9843999743461609,"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":0.9843999743461609,"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":0.008999999612569809,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/causal-representation-learning","display_name":"causal representation learning","score":0.9079999923706055},{"id":"https://openalex.org/keywords/unstructured-data","display_name":"unstructured data","score":0.5699999928474426},{"id":"https://openalex.org/keywords/image-observation","display_name":"image observation","score":0.5590000152587891},{"id":"https://openalex.org/keywords/autoencoder","display_name":"autoencoder","score":0.453000009059906},{"id":"https://openalex.org/keywords/identifiability","display_name":"identifiability","score":0.7979999780654907},{"id":"https://openalex.org/keywords/disentanglement","display_name":"disentanglement","score":0.7739999890327454},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.6830000281333923},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.9430000185966492},{"id":"https://openalex.org/keywords/forecasting","display_name":"forecasting","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8223999738693237},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.7440000176429749},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.6669999957084656},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.541700005531311},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5133000016212463},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5128999948501587},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4936000108718872},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39969998598098755},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39719998836517334},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35989999771118164},{"id":"https://openalex.org/C100279451","wikidata":"https://www.wikidata.org/wiki/Q372193","display_name":"Perplexity","level":3,"score":0.34299999475479126},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3287999927997589},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30480000376701355},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28610000014305115},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C162144332","wikidata":"https://www.wikidata.org/wiki/Q1665305","display_name":"Instrumental variable","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C27574286","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Variables","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C120567893","wikidata":"https://www.wikidata.org/wiki/Q1582085","display_name":"Knowledge extraction","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37083","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37083","pdf_url":"https://arxiv.org/pdf/2609.37083","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.2609.37083","doi":"https://doi.org/10.48550/arxiv.2609.37083","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37083","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:2609.37083","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37083","pdf_url":"https://arxiv.org/pdf/2609.37083","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/W7214930212.pdf","grobid_xml":"https://content.openalex.org/works/W7214930212.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W607590176","https://openalex.org/W2003945397","https://openalex.org/W2064675550","https://openalex.org/W2075860462","https://openalex.org/W2088440750","https://openalex.org/W2239232218","https://openalex.org/W2930380020","https://openalex.org/W3013638491","https://openalex.org/W3014869516","https://openalex.org/W3026310873","https://openalex.org/W3028073062","https://openalex.org/W3135318897","https://openalex.org/W3135588948","https://openalex.org/W3211856448"],"related_works":["https://openalex.org/W3010923896","https://openalex.org/W4312539268","https://openalex.org/W4399120457","https://openalex.org/W3174822621","https://openalex.org/W7165892340","https://openalex.org/W3186801389","https://openalex.org/W7204018036","https://openalex.org/W4308611018","https://openalex.org/W4387560199","https://openalex.org/W7136245311"],"abstract_inverted_index":{"We":[0,123],"study":[1],"the":[2,6,30,39,83,136,159,162,174],"problem":[3],"of":[4,9,29,114,138,161],"recovering":[5],"governing":[7],"ODE":[8,23,121],"a":[10,99,103,108,151],"dynamical":[11],"system":[12,153],"from":[13,55,141],"unstructured,":[14],"high-dimensional":[15,56],"observations":[16,57],"such":[17],"as":[18,73],"images.":[19],"Existing":[20],"methods":[21,49,164],"for":[22,126],"discovery":[24,77],"typically":[25,80],"assume":[26,81],"direct":[27],"measurements":[28],"variables,":[31],"or":[32],"do":[33],"not":[34],"provide":[35,50],"theoretical":[36],"guarantees":[37,51],"on":[38,52,147,158],"learned":[40],"variables":[41,54,68,84,115],"and":[42,150,165],"equations.":[43,89],"While":[44],"Causal":[45],"Representation":[46],"Learning":[47],"(CRL)":[48],"identifying":[53],"up":[58],"to":[59,75,87,119,134,143,173],"component-wise":[60,109],"diffeomorphisms,":[61],"we":[62,91],"show":[63,124,154],"that":[64,82,101,111,116,125,155,166,170],"in":[65],"general":[66],"these":[67],"cannot":[69],"be":[70],"used":[71],"directly":[72],"input":[74],"equation":[76],"methods,":[78],"which":[79],"will":[85],"lead":[86],"sparse":[88,120],"So":[90],"introduce":[92],"SParse":[93],"Equivalent":[94],"Equation":[95],"Discovery":[96],"AutoEncoder":[97],"(SPEED-AE),":[98],"framework":[100],"combines":[102],"pretrained":[104],"CRL":[105,163],"method":[106],"with":[107],"autoencoder":[110],"learns":[112],"transformations":[113],"are":[117,171],"amenable":[118],"discovery.":[122],"polynomial":[127,142],"ODEs,":[128],"this":[129],"additional":[130],"step":[131],"allows":[132],"us":[133],"restrict":[135],"identifiability":[137],"each":[139],"variable":[140],"monomial":[144],"diffeomorphisms.":[145],"Experiments":[146],"Lotka-Volterra,":[148],"Lorenz,":[149],"two-pendulum":[152],"SPEED-AE":[156],"improves":[157],"disentanglement":[160],"it":[167],"recovers":[168],"ODEs":[169],"closest":[172],"ground":[175],"truth,":[176],"while":[177],"achieving":[178],"state-of-the-art":[179],"forecasting":[180],"performance.":[181]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}