{"id":"https://openalex.org/W7148614101","doi":"https://doi.org/10.48550/arxiv.2604.00277","title":"Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics","display_name":"Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7148614101","doi":"https://doi.org/10.48550/arxiv.2604.00277"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2604.00277","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2604.00277","pdf_url":"https://arxiv.org/pdf/2604.00277","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W7148614101"],"child_works_count":0,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2604.00277","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114656704","display_name":"Simone Betteti","orcid":"https://orcid.org/0009-0000-3444-0838","observed_orcids":["https://orcid.org/0009-0000-3444-0838"]},"institutions":[{"id":"https://openalex.org/I4405266748","display_name":"The Italian Institute of Artificial Intelligence","ror":"https://ror.org/05afakd88","country_code":"IT","type":"government","lineage":["https://openalex.org/I4405266748"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Betteti, Simone","raw_affiliation_strings":["RIAS Lab The Italian Institute of Artificial Intelligence for Industry Turin , 10129 , IT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RIAS Lab The Italian Institute of Artificial Intelligence for Industry Turin , 10129 , IT","institution_ids":["https://openalex.org/I4405266748"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009660282","display_name":"Luca Laurenti","orcid":"https://orcid.org/0000-0003-1190-6097","observed_orcids":["https://orcid.org/0000-0003-1190-6097"]},"institutions":[{"id":"https://openalex.org/I4405266748","display_name":"The Italian Institute of Artificial Intelligence","ror":"https://ror.org/05afakd88","country_code":"IT","type":"government","lineage":["https://openalex.org/I4405266748"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["IT","NL"],"is_corresponding":false,"raw_author_name":"Laurenti, Luca","raw_affiliation_strings":["Delft Center for Systems and Control , TU Delft , Delft , 2600 AA , The Netherlands","RIAS Lab The Italian Institute of Artificial Intelligence for Industry Turin , 10129 , IT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control , TU Delft , Delft , 2600 AA , The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"RIAS Lab The Italian Institute of Artificial Intelligence for Industry Turin , 10129 , IT","institution_ids":["https://openalex.org/I4405266748"]}]}],"institutions":[],"countries_distinct_count":2,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.5092999935150146,"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"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.5092999935150146,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.3176000118255615,"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/T10320","display_name":"Neural Networks and Applications","score":0.06809999793767929,"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/energy-based-models","display_name":"energy-based models","score":0.9990000128746033},{"id":"https://openalex.org/keywords/physical-ai","display_name":"physical AI","score":0.7059999704360962},{"id":"https://openalex.org/keywords/system-identification","display_name":"system identification","score":0.8600000143051147},{"id":"https://openalex.org/keywords/port-hamiltonian-systems","display_name":"port-Hamiltonian systems","score":0.9200000166893005},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.8949999809265137},{"id":"https://openalex.org/keywords/dissipative-dynamics","display_name":"dissipative dynamics","score":0.7680000066757202},{"id":"https://openalex.org/keywords/multi-well-systems","display_name":"multi-well systems","score":0.6399999856948853},{"id":"https://openalex.org/keywords/ring-systems","display_name":"ring systems","score":0.7540000081062317},{"id":"https://openalex.org/keywords/safety-guarantees","display_name":"safety guarantees","score":0.5659999847412109}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5550000071525574},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5523999929428101},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.5054000020027161},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.47749999165534973},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4643000066280365},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4537999927997589},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4487999975681305},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.4481000006198883},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.420199990272522},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3779999911785126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35749998688697815},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35519999265670776},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.34790000319480896},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2646999955177307},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2604.00277","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2604.00277","pdf_url":"https://arxiv.org/pdf/2604.00277","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2604.00277","doi":"https://doi.org/10.48550/arxiv.2604.00277","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00277","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2604.00277","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2604.00277","pdf_url":"https://arxiv.org/pdf/2604.00277","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7148614101.pdf","grobid_xml":"https://content.openalex.org/works/W7148614101.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1557324374","https://openalex.org/W1984431842","https://openalex.org/W2000985550","https://openalex.org/W2062210787","https://openalex.org/W2112246162","https://openalex.org/W2128084896","https://openalex.org/W2158208985","https://openalex.org/W2169969507","https://openalex.org/W2412287113","https://openalex.org/W2436219157","https://openalex.org/W2587333550","https://openalex.org/W2800448691","https://openalex.org/W2808746463","https://openalex.org/W2889046694","https://openalex.org/W3011162163","https://openalex.org/W3122855748","https://openalex.org/W3127151792","https://openalex.org/W3175924829","https://openalex.org/W4212795191","https://openalex.org/W4223631735","https://openalex.org/W4246840991","https://openalex.org/W4285298244","https://openalex.org/W4389169589","https://openalex.org/W4396512244","https://openalex.org/W4407186835","https://openalex.org/W4410638676","https://openalex.org/W4415798553","https://openalex.org/W7133194308","https://openalex.org/W7133218158"],"related_works":["https://openalex.org/W7154593899","https://openalex.org/W4384008083","https://openalex.org/W4314947461","https://openalex.org/W4406053225","https://openalex.org/W7214968694","https://openalex.org/W3110785006","https://openalex.org/W4403787480","https://openalex.org/W7164873509","https://openalex.org/W7148065531","https://openalex.org/W2763778448"],"abstract_inverted_index":{"Energy-based":[0],"models":[1],"(EBMs)":[2],"implement":[3],"inference":[4],"as":[5],"gradient":[6],"descent":[7],"on":[8,146],"a":[9,107,118,122],"learned":[10],"Lyapunov":[11,68],"function,":[12],"yielding":[13],"interpretable,":[14],"structure-preserving":[15],"alternatives":[16],"to":[17,88,142],"black-box":[18],"neural":[19],"ODEs":[20],"and":[21,35,81,99,126,136,149,165],"aligning":[22],"naturally":[23],"with":[24,59,121,163],"physical":[25],"AI.":[26],"Yet":[27],"their":[28],"use":[29],"in":[30,110],"system":[31,57],"identification":[32,58],"remains":[33],"limited,":[34],"existing":[36],"architectures":[37],"lack":[38],"formal":[39],"stability":[40],"guarantees":[41,140,168],"that":[42,138],"globally":[43],"preclude":[44],"unstable":[45],"modes.":[46],"We":[47,84],"address":[48],"this":[49],"gap":[50],"by":[51,91,169],"introducing":[52],"an":[53],"EBM":[54,86,159],"framework":[55],"for":[56,103],"stable,":[60],"dissipative,":[61],"absorbing":[62,70,131],"invariant":[63],"dynamics.":[64],"Unlike":[65],"classical":[66],"global":[67],"stability,":[69],"invariance":[71,132],"expands":[72],"the":[73,153],"class":[74],"of":[75],"stability-preserving":[76],"architectures,":[77],"enabling":[78],"more":[79],"flexible":[80],"expressive":[82],"EBMs.":[83,112,144],"extend":[85,141],"theory":[87],"nonsmooth":[89],"activations":[90],"establishing":[92],"negative":[93],"energy":[94],"dissipation":[95],"via":[96],"Clarke":[97],"derivatives":[98],"deriving":[100],"new":[101],"conditions":[102],"radial":[104],"unboundedness,":[105],"exposing":[106],"stability-expressivity":[108],"tradeoff":[109],"standard":[111],"To":[113],"overcome":[114],"this,":[115],"we":[116],"introduce":[117],"hybrid":[119,158],"architecture":[120,160],"dynamical":[123],"visible":[124],"layer":[125],"static":[127],"hidden":[128],"layers,":[129],"prove":[130],"under":[133],"mild":[134],"assumptions,":[135],"show":[137],"these":[139],"port-Hamiltonian":[143],"Experiments":[145],"metric-deformed":[147],"multi-well":[148],"ring":[150],"systems":[151],"validate":[152],"approach,":[154],"showcasing":[155],"how":[156],"our":[157],"combines":[161],"expressivity":[162],"sound":[164],"provable":[166],"safety":[167],"design.":[170]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-04-03T00:00:00"}
