{"id":"https://openalex.org/W4414769089","doi":"https://doi.org/10.48550/arxiv.2505.00782","title":"Dynamical System Parameter Path Optimization using Persistent Homology","display_name":"Dynamical System Parameter Path Optimization using Persistent Homology","publication_year":2025,"publication_date":"2025-05-01","ids":{"openalex":"https://openalex.org/W4414769089","doi":"https://doi.org/10.48550/arxiv.2505.00782"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.00782","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.00782","pdf_url":"https://arxiv.org/pdf/2505.00782","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.00782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026252787","display_name":"Max M. Chumley","orcid":"https://orcid.org/0000-0002-5335-5409"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chumley, Max M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030913569","display_name":"Firas A. Khasawneh","orcid":"https://orcid.org/0000-0001-7817-7445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khasawneh, Firas A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T13067","display_name":"Geological Modeling and Analysis","score":0.9334999918937683,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13067","display_name":"Geological Modeling and Analysis","score":0.9334999918937683,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7337999939918518},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.6362000107765198},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5925999879837036},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5511999726295471},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.5284000039100647},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.5123000144958496},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4546999931335449},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4523000121116638},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45179998874664307},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4325999915599823}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7337999939918518},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.6362000107765198},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5925999879837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5853999853134155},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5511999726295471},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.5284000039100647},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5123000144958496},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4546999931335449},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45179998874664307},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4212000072002411},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.32600000500679016},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.3154999911785126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30239999294281006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3012999892234802},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C24977911","wikidata":"https://www.wikidata.org/wiki/Q1491995","display_name":"Connected space","level":3,"score":0.29660001397132874},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C90738871","wikidata":"https://www.wikidata.org/wiki/Q41642869","display_name":"Configuration space","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C2777391479","wikidata":"https://www.wikidata.org/wiki/Q5178040","display_name":"Coupling parameter","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.27399998903274536},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C154804608","wikidata":"https://www.wikidata.org/wiki/Q2721559","display_name":"Topological manifold","level":5,"score":0.25839999318122864},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C47600822","wikidata":"https://www.wikidata.org/wiki/Q7825032","display_name":"Topological dynamics","level":5,"score":0.251800000667572},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.00782","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.00782","pdf_url":"https://arxiv.org/pdf/2505.00782","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2505.00782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.00782","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.00782","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.00782","pdf_url":"https://arxiv.org/pdf/2505.00782","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Nonlinear":[0],"dynamical":[1,80,119,178],"systems":[2,9,17,179],"are":[3,18,31],"complex":[4],"and":[5,27,121,180,189],"typically":[6],"only":[7],"simple":[8],"can":[10],"be":[11],"analytically":[12],"studied.":[13],"In":[14,42,68],"applications,":[15],"these":[16],"usually":[19],"defined":[20,161],"with":[21],"a":[22,43,62,73,79,101,118,141,151,168],"set":[23,152],"of":[24,96,117,153,170],"tunable":[25],"parameters":[26,30,59,154],"as":[28],"the":[29,33,57,94,113,132,148,157,163,174,193],"varied":[32],"system":[34,58,64,81,120,149],"response":[35,65,116],"undergoes":[36],"significant":[37],"topological":[38,88,102,110,159],"changes":[39],"or":[40,66,107],"bifurcations.":[41],"high":[44],"dimensional":[45],"parameter":[46,82,133],"space,":[47],"it":[48],"is":[49,85,140],"difficult":[50],"to":[51,55,60,99,125,135,150,176,182,185,191,195],"determine":[52],"which":[53],"direction":[54],"vary":[56],"achieve":[61,196],"desired":[63,158],"state.":[67],"this":[69,144],"paper,":[70],"we":[71,92],"introduce":[72],"new":[74],"approach":[75],"for":[76,104],"optimally":[77,126],"navigating":[78],"space":[83,115,134,145],"that":[84,146,155],"rooted":[86],"in":[87,112,131,143],"data":[89],"analysis.":[90],"Specifically":[91],"use":[93,122],"differentiability":[95],"persistence":[97],"diagrams":[98],"define":[100],"language":[103],"intuitively":[105],"promoting":[106],"deterring":[108],"different":[109,177,187,197],"features":[111,160,188],"state":[114],"gradient":[123],"descent":[124],"move":[127],"from":[128],"one":[129],"point":[130],"another.":[136],"The":[137],"end":[138],"result":[139],"path":[142],"guides":[147],"yield":[156],"by":[162,172],"loss":[164],"function.":[165],"We":[166],"show":[167],"number":[169],"examples":[171],"applying":[173],"methods":[175],"scenarios":[181],"demonstrate":[183],"how":[184,190],"promote":[186],"choose":[192],"hyperparameters":[194],"outcomes.":[198]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
