{"id":"https://openalex.org/W4363620352","doi":"https://doi.org/10.1109/ciss56502.2023.10089728","title":"Tunable complexity benchmarks for evaluating physics-informed neural networks on coupled ordinary differential equations","display_name":"Tunable complexity benchmarks for evaluating physics-informed neural networks on coupled ordinary differential equations","publication_year":2023,"publication_date":"2023-03-22","ids":{"openalex":"https://openalex.org/W4363620352","doi":"https://doi.org/10.1109/ciss56502.2023.10089728"},"language":"en","primary_location":{"id":"doi:10.1109/ciss56502.2023.10089728","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss56502.2023.10089728","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 57th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035926574","display_name":"Alexander New","orcid":"https://orcid.org/0000-0001-8369-1473"},"institutions":[{"id":"https://openalex.org/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander New","raw_affiliation_strings":["Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044","institution_ids":["https://openalex.org/I2802946424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027840817","display_name":"Benjamin Eng","orcid":null},"institutions":[{"id":"https://openalex.org/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Eng","raw_affiliation_strings":["Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044","institution_ids":["https://openalex.org/I2802946424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048872081","display_name":"Andrea C. Timm","orcid":"https://orcid.org/0000-0002-0570-9217"},"institutions":[{"id":"https://openalex.org/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea C. Timm","raw_affiliation_strings":["Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044","institution_ids":["https://openalex.org/I2802946424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060107950","display_name":"Andrew S. Gearhart","orcid":"https://orcid.org/0000-0002-9597-6086"},"institutions":[{"id":"https://openalex.org/I2802946424","display_name":"Johns Hopkins University Applied Physics Laboratory","ror":"https://ror.org/029pp9z10","country_code":"US","type":"facility","lineage":["https://openalex.org/I145311948","https://openalex.org/I2802946424"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew S. Gearhart","raw_affiliation_strings":["Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University,Applied Physics Laboratory,Research and Exploratory Development Department,Laurel,Maryland,21044","institution_ids":["https://openalex.org/I2802946424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3107,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51269555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9553999900817871,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11222","display_name":"Magnetic Properties and Applications","score":0.9297000169754028,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6721217632293701},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6291208267211914},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6186915636062622},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.615649938583374},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5363565683364868},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.49174264073371887},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.48471617698669434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47991880774497986},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4399045407772064},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43271759152412415},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4236689805984497},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4162255525588989},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39015766978263855},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34870320558547974},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32278215885162354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32013222575187683},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21074000000953674},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2069539725780487},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16601163148880005}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6721217632293701},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6291208267211914},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6186915636062622},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.615649938583374},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5363565683364868},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.49174264073371887},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.48471617698669434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47991880774497986},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4399045407772064},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43271759152412415},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4236689805984497},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4162255525588989},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39015766978263855},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34870320558547974},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32278215885162354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32013222575187683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21074000000953674},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2069539725780487},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16601163148880005},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ciss56502.2023.10089728","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss56502.2023.10089728","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 57th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1528042669","https://openalex.org/W1940321820","https://openalex.org/W2006903949","https://openalex.org/W2046738125","https://openalex.org/W2137983211","https://openalex.org/W2144144709","https://openalex.org/W2194775991","https://openalex.org/W2809090039","https://openalex.org/W2899283552","https://openalex.org/W2962727772","https://openalex.org/W2963477238","https://openalex.org/W2964121744","https://openalex.org/W3014009018","https://openalex.org/W3031420959","https://openalex.org/W3041682155","https://openalex.org/W3047168498","https://openalex.org/W3093786597","https://openalex.org/W3138582970","https://openalex.org/W3163993681","https://openalex.org/W3170733857","https://openalex.org/W3195143696","https://openalex.org/W3195738678","https://openalex.org/W3197694049","https://openalex.org/W3200673624","https://openalex.org/W3205073660","https://openalex.org/W3211426055","https://openalex.org/W4226448861","https://openalex.org/W4283314437","https://openalex.org/W4286988446","https://openalex.org/W4287072668","https://openalex.org/W4287671439","https://openalex.org/W4302305146","https://openalex.org/W4311906773","https://openalex.org/W6638908295","https://openalex.org/W6748304690","https://openalex.org/W6752495264","https://openalex.org/W6800781246"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W2489516236"],"abstract_inverted_index":{"In":[0],"this":[1,92],"work,":[2],"we":[3,62],"assess":[4],"the":[5,82,95,104,113,116],"ability":[6],"of":[7,25,35,79,84,103,115],"physics-informed":[8],"neural":[9],"networks":[10],"(PINNs)":[11],"to":[12,68,72],"solve":[13],"increasingly-complex":[14],"coupled":[15],"ordinary":[16],"differential":[17,29],"equations":[18,30,80],"(ODEs).":[19],"We":[20,87],"focus":[21],"on":[22],"a":[23,38,52],"pair":[24],"benchmarks:":[26],"discretized":[27],"partial":[28],"and":[31,50,81,106],"harmonic":[32],"oscillators,":[33],"each":[34],"which":[36],"has":[37],"tunable":[39],"parameter":[40],"that":[41,56,64],"controls":[42],"its":[43],"complexity.":[44],"Even":[45],"by":[46,112],"varying":[47],"network":[48,99],"architecture":[49],"applying":[51],"state-of-the-art":[53],"training":[54,60],"method":[55],"accounts":[57],"for":[58],"\u201cdifficult\u201d":[59],"regions,":[61],"show":[63],"PINNs":[65],"eventually":[66],"fail":[67],"produce":[69],"correct":[70],"solutions":[71],"these":[73],"benchmarks":[74],"as":[75,110],"their":[76],"complexity-the":[77],"number":[78],"size":[83],"time":[85],"domain-increases.":[86],"identify":[88],"several":[89],"reasons":[90],"why":[91],"may":[93],"be":[94],"case,":[96],"including":[97],"insufficient":[98],"capacity,":[100],"poor":[101],"conditioning":[102],"ODEs,":[105],"high":[107],"local":[108],"curvature,":[109],"measured":[111],"Laplacian":[114],"PINN":[117],"loss.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
