{"id":"https://openalex.org/W7165784318","doi":"https://doi.org/10.48550/arxiv.2606.24769","title":"Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems","display_name":"Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165784318","doi":"https://doi.org/10.48550/arxiv.2606.24769"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24769","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24769","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.24769","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135197851","display_name":"Matteo Raviola","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raviola, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027402421","display_name":"Benjamin Peherstorfer","orcid":"https://orcid.org/0000-0002-1558-6775"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peherstorfer, Benjamin","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":0.48750001192092896,"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":0.48750001192092896,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.08910000324249268,"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 methods for differential equations","score":0.06340000033378601,"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/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.6664999723434448},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.617900013923645},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.6068000197410583},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5863999724388123},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5662000179290771},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5422000288963318},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.46239998936653137}],"concepts":[{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.617900013923645},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.6068000197410583},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5863999724388123},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5662000179290771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.558899998664856},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5422000288963318},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.382099986076355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36480000615119934},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C10238366","wikidata":"https://www.wikidata.org/wiki/Q165618","display_name":"Moment of inertia","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29170000553131104},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.28839999437332153}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24769","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24769","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.24769","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24769","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Even":[0],"when":[1],"Dirac-Frenkel":[2,39,71,108],"dynamics":[3,14,40,82],"determine":[4],"a":[5,85],"well-defined":[6],"evolution":[7],"in":[8,56],"function":[9],"space,":[10],"the":[11,38,53,70,76,92,95,98,112,122],"corresponding":[12],"parameter":[13,47,64,81],"can":[15],"be":[16],"non-unique":[17],"or":[18,29],"ill-conditioned":[19],"for":[20],"redundant":[21],"nonlinear":[22],"parametrizations,":[23],"such":[24],"as":[25,106,116],"typical":[26],"neural":[27],"networks":[28],"mixture":[30],"models.":[31],"We":[32,73],"propose":[33],"to":[34,37,50,68],"add":[35],"inertia":[36],"and":[41,83],"show":[42],"that":[43,58,75],"this":[44],"allows":[45],"useful":[46],"velocity":[48,65,114],"information":[49],"persist":[51],"from":[52],"past":[54],"trajectory":[55],"directions":[57,66],"are":[59],"weakly":[60],"informed,":[61],"while":[62],"well-informed":[63],"continue":[67],"follow":[69],"dynamics.":[72],"prove":[74],"inertial":[77],"formulation":[78],"yields":[79],"well-posed":[80],"provide":[84],"posteriori":[86],"error":[87],"bounds.":[88],"After":[89],"time":[90],"discretization,":[91],"method":[93],"requires":[94],"solution":[96],"of":[97,101],"same":[99],"type":[100],"regularized":[102],"linear":[103],"least-squares":[104],"problem":[105],"standard":[107],"dynamics,":[109],"but":[110],"with":[111,126],"previous":[113],"appearing":[115],"an":[117],"anchor.":[118],"Numerical":[119],"experiments":[120],"demonstrate":[121],"increased":[123],"robustness":[124],"obtained":[125],"inertia.":[127]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-25T00:00:00"}