{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T03:12:49Z","timestamp":1780456369890,"version":"3.54.1"},"reference-count":46,"publisher":"Informa UK Limited","issue":"4","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2143695"],"award-info":[{"award-number":["2143695"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Technometrics"],"published-print":{"date-parts":[[2023,10,2]]},"DOI":"10.1080\/00401706.2023.2203175","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T19:53:10Z","timestamp":1681761190000},"page":"564-578","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":3,"title":["Statistical Learning for Nonlinear Dynamical Systems with Applications to Aircraft-UAV Collisions"],"prefix":"10.1080","volume":"65","author":[{"given":"Xinchao","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, University of Arkansas, Fayetteville, AR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Arkansas, Fayetteville, AR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tulin","family":"Kaman","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohua","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guang","family":"Lin","sequence":"additional","affiliation":[{"name":"Departments of Mathematics, Statistics & School of Mechanical Engineering, Purdue University, West Lafayette, IN"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"301","published-online":{"date-parts":[[2023,5,30]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/2015WR016967"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"e_1_3_3_4_1","unstructured":"CFR (2012) \u201cCode of Federal Regulations: 14 CFR 25.631-Bird Strike Damage \u201d available at https:\/\/www.ecfr.gov\/current\/title-14\/chapter-I\/ subchapter-C\/part-25\/subpart-D\/subject-group-ECFRff93ea3edba9270\/section-25.631."},{"key":"e_1_3_3_5_1","doi-asserted-by":"crossref","unstructured":"Chen G. and Tuo R. (2022) \u201cProjection Pursuit Gaussian Process Regression \u201d arXiv:2004.00667.","DOI":"10.1080\/24725854.2022.2121882"},{"key":"e_1_3_3_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2020.1817790"},{"key":"e_1_3_3_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2020.1801255"},{"key":"e_1_3_3_8_1","unstructured":"Chen X. L. Duan J. and Karniadakis G. E. (2019) \u201cLearning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements \u201d arXiv: 1910.09098."},{"key":"e_1_3_3_9_1","volume-title":"Statistics for Spatio-Temporal Data","author":"Cressie N.","year":"2011","unstructured":"Cressie, N., and Wikle, C. (2011), Statistics for Spatio-Temporal Data, Hoboken, NJ: Wiley."},{"key":"e_1_3_3_10_1","unstructured":"D\u2019Elia M. (2019) \u201cnPINNs: Physics-Informed Neural Networks \u201d in Control and Optimization for Nonlocal Problem RICAM Linz Austria."},{"key":"e_1_3_3_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2016.1211554"},{"key":"e_1_3_3_12_1","unstructured":"FAA (2014) \u201cFAA UAS Accident and Incident Preliminary Reports \u201d available at https:\/\/www.asias.faa.gov\/apex\/f?p=100:446:::NO:446::."},{"key":"e_1_3_3_13_1","unstructured":"FAA (2020) \u201cUAS by the Numbers \u201d available at https:\/\/www. faa.gov\/uas\/resources\/."},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780367815493"},{"key":"e_1_3_3_15_1","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOAS934"},{"key":"e_1_3_3_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.2018.1474689"},{"key":"e_1_3_3_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2018.07.017"},{"key":"e_1_3_3_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2013.869263"},{"key":"e_1_3_3_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asv002"},{"key":"e_1_3_3_20_1","doi-asserted-by":"publisher","DOI":"10.7771\/2159-6670.1117"},{"key":"e_1_3_3_21_1","volume-title":"Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA","author":"Krainski E. T.","year":"2019","unstructured":"Krainski, E. T., Gomez-Rubio, V., Bakka, H., Lenzi, A., Castro-Camilo, D., Simpson, D., Lindgren, F., and Rue, H. (2019), Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA, Boca Raton, FL: Chapman and Hall\/CRC."},{"key":"e_1_3_3_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1157702"},{"key":"e_1_3_3_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33287-6"},{"key":"e_1_3_3_24_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2011.00777.x"},{"key":"e_1_3_3_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1863223"},{"key":"e_1_3_3_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2020.105713"},{"key":"e_1_3_3_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2021.107078"},{"key":"e_1_3_3_28_1","first-page":"166","volume-title":"Atmospheric Turbulence and Radio Wave Propagation","author":"Lumley J. L.","year":"1967","unstructured":"Lumley, J. L. (1967), \u201cThe Structure of Inhomogeneous Turbulent Flows,\u201d in Atmospheric Turbulence and Radio Wave Propagation, eds. A. M. Yaglom and V. I. Tartarsky, pp. 166\u2013177."},{"key":"e_1_3_3_29_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1409123"},{"key":"e_1_3_3_30_1","unstructured":"Olivares G. (2017) \u201cASSURE UAS Airborne Collision Severity Evaluation Final Report \u201d available at https:\/\/www.assureuas.org\/projects\/ completed\/sUASAirborneCollisionReport.php."},{"key":"e_1_3_3_31_1","unstructured":"Olivares G. Lacy T. E. Gomez L. de los Monteros J. E. Baldridge R. J. Zinzuwadia C. M. Aldag T. Kota K. R. Ricks T. M. and Jayakody N. (2017) \u201cUAS Airborne Collision Severity Evaluation: Executive Summary \u2013 Structural Evaluation\u201d \u201d Report number: ASSURE-AC-01. Available at http:\/\/www.assureuas.org\/projects\/deliverables\/sUASAirborneCollisionReport.php."},{"key":"e_1_3_3_32_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1229845"},{"key":"e_1_3_3_33_1","doi-asserted-by":"crossref","unstructured":"Qian E. Karamer B. Peherstorfer B. and Willcox K. (2019) \u201cLift&Learn: Physics-Informed Machine Learning for Large-Scale Nonlinear Dynamical Systems \u201d Oden Institute Report 19-18.","DOI":"10.1016\/j.physd.2020.132401"},{"key":"e_1_3_3_34_1","first-page":"1","article-title":"\u201cDeep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations,\u201d","volume":"19","author":"Raissi M.","year":"2018","unstructured":"Raissi, M. (2018), \u201cDeep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations,\u201d Journal of Machine Learning Research, 19, 1\u201324.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_3_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.11.039"},{"key":"e_1_3_3_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"e_1_3_3_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.07.050"},{"key":"e_1_3_3_38_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1120762"},{"key":"e_1_3_3_39_1","doi-asserted-by":"crossref","unstructured":"Sauer A. Gramacy R. B. and Higdon D. (2021) \u201cActive Learning for Deep Gaussian Process Surrogates \u201d arXiv:2012.08015.","DOI":"10.1201\/9780367815493"},{"key":"e_1_3_3_40_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12061"},{"key":"e_1_3_3_41_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2021.2024453"},{"key":"e_1_3_3_42_1","doi-asserted-by":"crossref","unstructured":"Swischuk R. Kramer B. Huang C. and Willcox K. (2019a) \u201cLearning Physics-based Reduced-Order Models for a Single-Injector Combustion Process \u201d arXiv: 1908.03620.","DOI":"10.2514\/6.2020-1411"},{"key":"e_1_3_3_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2018.07.021"},{"key":"e_1_3_3_44_1","doi-asserted-by":"publisher","DOI":"10.1080\/24725854.2021.1891485"},{"key":"e_1_3_3_45_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118382011"},{"key":"e_1_3_3_46_1","unstructured":"Zhang B. Y. Cole D. A. and Gramacy R. B. (2021a) \u201cDistance-Distributed Design for Gaussian Process Surrogates \u201d arXiv:1812.02794."},{"key":"e_1_3_3_47_1","doi-asserted-by":"crossref","unstructured":"Zhang R. D. Mak S. and Dunson D. (2021b) \u201cGaussian Process Subspace Regression for Model Reduction \u201d arXiv:2107.04668.","DOI":"10.26226\/morressier.612f6739bc98103724100999"}],"container-title":["Technometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/00401706.2023.2203175","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T12:41:48Z","timestamp":1699015308000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/00401706.2023.2203175"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,30]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,10,2]]}},"alternative-id":["10.1080\/00401706.2023.2203175"],"URL":"https:\/\/doi.org\/10.1080\/00401706.2023.2203175","relation":{},"ISSN":["0040-1706","1537-2723"],"issn-type":[{"value":"0040-1706","type":"print"},{"value":"1537-2723","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,30]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=utch20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=utch20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2021-12-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-04-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-05-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}