{"id":"https://openalex.org/W7204216702","doi":null,"title":"Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields","display_name":"Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields","publication_year":2026,"publication_date":"2026-08-18","ids":{"openalex":"https://openalex.org/W7204216702"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.18004","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18004","pdf_url":"https://arxiv.org/pdf/2608.18004","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.18004","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148114746","display_name":"Yixuan Sun","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sun, Yixuan","raw_affiliation_strings":["Mathematics and Computer Science , Argonne National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science , Argonne National Laboratory","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081693340","display_name":"Anirban Samaddar","orcid":"https://orcid.org/0000-0001-9520-8012","observed_orcids":["https://orcid.org/0000-0001-9520-8012"]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samaddar, Anirban","raw_affiliation_strings":["Mathematics and Computer Science , Argonne National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science , Argonne National Laboratory","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004608167","display_name":"Sandeep Madireddy","orcid":"https://orcid.org/0000-0002-0437-8655","observed_orcids":["https://orcid.org/0000-0002-0437-8655"]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madireddy, Sandeep","raw_affiliation_strings":["Mathematics and Computer Science , Argonne National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science , Argonne National Laboratory","institution_ids":["https://openalex.org/I1282105669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1282105669"],"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":0.9848999977111816,"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":0.9848999977111816,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.006300000008195639,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0035000001080334187,"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/flow-matching","display_name":"flow matching","score":0.921999990940094},{"id":"https://openalex.org/keywords/energy-based-models","display_name":"energy-based models","score":0.9779999852180481},{"id":"https://openalex.org/keywords/physics-informed-machine-learning","display_name":"physics-informed machine learning","score":0.5809999704360962},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.7570000290870667},{"id":"https://openalex.org/keywords/out-of-distribution-detection","display_name":"out-of-distribution detection","score":0.8560000061988831},{"id":"https://openalex.org/keywords/inverse-problems","display_name":"inverse problems","score":0.9300000071525574},{"id":"https://openalex.org/keywords/posterior-sampling","display_name":"posterior sampling","score":0.6110000014305115},{"id":"https://openalex.org/keywords/energy-mix","display_name":"energy mix","score":0.40799999237060547},{"id":"https://openalex.org/keywords/spectral-distance","display_name":"spectral distance","score":0.47999998927116394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5697000026702881},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4456999897956848},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44179999828338623},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41449999809265137},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40230000019073486},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3668999969959259},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.34470000863075256},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.33309999108314514},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.31130000948905945},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27869999408721924},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.2734000086784363},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25540000200271606},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:2608.18004","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18004","pdf_url":"https://arxiv.org/pdf/2608.18004","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.18004","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.18004","pdf_url":"https://arxiv.org/pdf/2608.18004","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/W7204216702.pdf","grobid_xml":"https://content.openalex.org/works/W7204216702.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W2416272112","https://openalex.org/W2531327146","https://openalex.org/W2808746463","https://openalex.org/W2913446963","https://openalex.org/W2938608316","https://openalex.org/W2959300817","https://openalex.org/W2980402966","https://openalex.org/W2994434574","https://openalex.org/W2995926841","https://openalex.org/W3010486187","https://openalex.org/W3101367735","https://openalex.org/W3110257065","https://openalex.org/W3112951692","https://openalex.org/W3119280808","https://openalex.org/W3162926177","https://openalex.org/W4297676498","https://openalex.org/W4298184813","https://openalex.org/W4302011821","https://openalex.org/W4303647933","https://openalex.org/W4319050105","https://openalex.org/W4321650217","https://openalex.org/W4378768721","https://openalex.org/W4379538539","https://openalex.org/W4391555771","https://openalex.org/W4399794913","https://openalex.org/W4399913033","https://openalex.org/W4403840763","https://openalex.org/W4405035048","https://openalex.org/W4405089005","https://openalex.org/W4407759809","https://openalex.org/W4414577602","https://openalex.org/W4414928250","https://openalex.org/W4415065481","https://openalex.org/W4415314511","https://openalex.org/W4415800802","https://openalex.org/W4416053722","https://openalex.org/W4416075215","https://openalex.org/W4416258139","https://openalex.org/W6910479752","https://openalex.org/W7077960107","https://openalex.org/W7083814721","https://openalex.org/W7133213777","https://openalex.org/W7133244780"],"related_works":["https://openalex.org/W4416053722","https://openalex.org/W4415065481","https://openalex.org/W4402706486","https://openalex.org/W4406072723","https://openalex.org/W3035281230","https://openalex.org/W7213371721","https://openalex.org/W4416788817","https://openalex.org/W3215182461","https://openalex.org/W3035326363","https://openalex.org/W7155587972"],"abstract_inverted_index":{"Probabilistic":[0],"modeling":[1],"of":[2,243],"physical":[3,13],"fields":[4],"benefits":[5],"from":[6,47,102,133],"both":[7],"a":[8,24,64,114,134,145,228,234],"data-driven":[9],"prior":[10],"and":[11,45,84,121,152,179,195],"known":[12],"structure":[14],"such":[15],"as":[16,144,201,238],"the":[17,50,80,87,92,103,122,125,130,164,172,184,192,215,225],"governing":[18],"equations.":[19],"Energy-based":[20],"models":[21,62],"(EBMs)":[22],"are":[23,99],"natural":[25],"fit":[26],"since":[27],"energies":[28],"compose":[29],"additively,":[30],"which":[31,85],"enables":[32],"augmenting":[33],"physics":[34],"information":[35],"during":[36],"inference.":[37],"However,":[38],"EBMs":[39],"have":[40],"been":[41],"difficult":[42],"to":[43,49,129,183,204,217],"train":[44],"sample":[46],"due":[48],"intractable":[51],"partition":[52],"function.":[53],"We":[54],"show":[55,163],"in":[56,171],"this":[57],"work":[58],"that":[59,232],"flow":[60,126,185],"matching":[61,104],"with":[63,227],"potential-induced":[65],"velocity":[66],"yield":[67],"an":[68,108,239],"explicit":[69,165],"scalar":[70],"energy":[71,97,131,143,153,166,194,197,226],"at":[72,91],"all":[73],"transport":[74],"times,":[75],"whose":[76],"gradient":[77],"is":[78],"exactly":[79],"converted":[81],"learned":[82],"score":[83],"recovers":[86],"marginal":[88],"negative":[89],"log-density":[90],"population":[93],"optimum.":[94],"The":[95],"time-dependent":[96],"functions":[98],"obtained":[100],"purely":[101],"regression":[105],"objective":[106],"on":[107],"independent":[109],"linear":[110],"Gaussian":[111],"interpolation,":[112],"without":[113],"variational":[115],"form":[116],"or":[117],"additional":[118],"MCMC":[119,169],"steps,":[120],"sampling":[123,156,174],"retains":[124],"ODE.":[127],"Access":[128],"function":[132,147],"trained":[135],"model":[136],"serves":[137],"three":[138],"roles:":[139],"energy-corrected":[140],"data":[141,193],"generation,":[142],"scoring":[146],"for":[148,157,208,220],"out-of-distribution":[149],"(OOD)":[150],"detection,":[151],"compositional":[154],"posterior":[155,235],"inverse":[158,221],"problems.":[159],"In":[160,211],"particular,":[161],"we":[162,189,213],"permits":[167],"general":[168],"samplers":[170],"predictor-corrector":[173],"framework,":[175],"reducing":[176],"PDE":[177,199],"residual":[178],"spectral":[180],"distance":[181],"compared":[182],"ODE":[186],"baseline.":[187],"Furthermore,":[188],"demonstrate":[190],"utilizing":[191],"physics-based":[196],"(e.g.,":[198],"residuals)":[200],"complementary":[202],"mechanisms":[203],"improve":[205],"detection":[206],"accuracy":[207],"OOD":[209],"tasks.":[210],"addition,":[212],"explore":[214],"connection":[216],"MCMC-based":[218],"inference":[219],"problems":[222],"by":[223],"composing":[224],"quadratic":[229],"observational":[230],"likelihood":[231],"yields":[233],"energy,":[236],"used":[237],"explicitly":[240],"chosen":[241],"family":[242],"inference-time":[244],"targets.":[245]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-26T00:00:00"}