{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:25:06Z","timestamp":1773015906697,"version":"3.50.1"},"reference-count":72,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"content-version":"am","delay-in-days":12,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"content-version":"vor","delay-in-days":12,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T017899\/1"],"award-info":[{"award-number":["EP\/T017899\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS\u20102231482"],"award-info":[{"award-number":["DMS\u20102231482"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DGE\u20102137100"],"award-info":[{"award-number":["DGE\u20102137100"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2342344"],"award-info":[{"award-number":["2342344"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020415","name":"Additional Ventures","doi-asserted-by":"publisher","award":["1449780"],"award-info":[{"award-number":["1449780"]}],"id":[{"id":"10.13039\/100020415","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numer Methods Biomed Eng"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>There are many computational models set up to predict blood flow and pressure in vascular networks. Methods for a single forward solution of such models are well established but become problematic in clinical applications, where model calibration and patient\u2010specific parameter estimation call for repeated forward simulations of the model requiring substantial computational costs. A potential workaround is emulation, which approximates the original mathematical model by a statistical or machine learning surrogate model. Our methodological framework is based on physics\u2010informed neural networks, with a particular focus on patient\u2010specific model calibration. Once fully trained, our machine learning model predicts flow and pressure waveforms in a fraction of the time required by the numerical solver, enabling fast parameter inference and inverse uncertainty quantification. The proposed framework is applied to clinical data from four patients diagnosed with a Double Outlet Right Ventricle (DORV), a congenital heart defect where both the aorta and main pulmonary artery connect to the right ventricle, potentially leading to insufficient oxygen delivery to the body and hence requiring careful blood flow monitoring. We assess the performance of our method in a comparative evaluation study that includes several alternative state\u2010of\u2010the\u2010art machine learning methods, and we quantify the improvement achieved in terms of accuracy and efficiency gains.<\/jats:p>","DOI":"10.1002\/cnm.70147","type":"journal-article","created":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T05:36:15Z","timestamp":1771047375000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Physics\u2010Informed Emulation of Systemic Circulation for Fast Parameter Estimation and Uncertainty Quantification"],"prefix":"10.1002","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6379-2186","authenticated-orcid":false,"given":"William","family":"Ryan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, University of Glasgow  Glasgow UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6282-9426","authenticated-orcid":false,"given":"Alyssa","family":"Taylor\u2010LaPole","sequence":"additional","affiliation":[{"name":"Rice University  Houston Texas USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2694-0044","authenticated-orcid":false,"given":"Mette","family":"Olufsen","sequence":"additional","affiliation":[{"name":"North Carolina State University  Raleigh North Carolina USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dirk","family":"Husmeier","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Glasgow  Glasgow UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladislav","family":"Vyshemirskiy","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Glasgow  Glasgow UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.medengphy.2012.08.009"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00241.2020"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2010.12.003"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1114\/1.1326031"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598\u2010018\u201035344\u20100"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1161\/CIR.0000000000000696"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1136\/thx.26.3.240"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.010908.165248"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237\u2010024\u201001875\u2010x"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3421"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0101128"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.201121"},{"key":"e_1_2_12_14_1","unstructured":"M.Raissi A.Yazdani andG. E.Karniadakis \u201cHidden Fluid Mechanics: A Navier\u2013Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data \u201d2018."},{"key":"e_1_2_12_15_1","unstructured":"J.Garay J.Dunstan S.Uribe andF.Sahli Costabal \u201cPhysics\u2010Informed Neural Networks for Blood Flow Inverse Problems \u201d2023."},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112623"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109913"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.taml.2020.01.031"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113703"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112732"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.3390\/computation12030041"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.115671"},{"key":"e_1_2_12_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/22M1527763"},{"key":"e_1_2_12_24_1","unstructured":"A.Daw J.Bu S.Wang P.Perdikaris andA.Karpatne \u201cMitigating Propagation Failures in Physics\u2010Informed Neural Networks Using Retain\u2010Resample\u2010Release (r3) Sampling \u201dinProceedings of the 40th International Conference on Machine Learning(PMLR 2023) 7264\u20137302."},{"issue":"402","key":"e_1_2_12_25_1","first-page":"1","article-title":"Piratenets: Physics\u2010Informed Deep Learning With Residual Adaptive Networks","volume":"25","author":"Wang S.","year":"2024","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113708"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113698"},{"key":"e_1_2_12_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2025.113799"},{"key":"e_1_2_12_29_1","doi-asserted-by":"crossref","unstructured":"R. M.Neal \u201cMCMC Using Hamiltonian Dynamics \u201d2011 https:\/\/doi.org\/10.1201\/b10905.","DOI":"10.1201\/b10905-6"},{"key":"e_1_2_12_30_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2024.0663"},{"key":"e_1_2_12_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117193"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev\u2010bioeng\u2010100219\u2010110055"},{"issue":"2","key":"e_1_2_12_33_1","article-title":"4d Flow Imaging With MRI","volume":"4","author":"Stankovic Z.","year":"2014","journal-title":"Cardiovascular Diagnosis & Therapy"},{"key":"e_1_2_12_34_1","first-page":"263","volume-title":"Selected Papers Volume I","author":"Lax P.","year":"2005"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237-022-01650-w"},{"key":"e_1_2_12_36_1","doi-asserted-by":"publisher","DOI":"10.3390\/fluids8020046"},{"key":"e_1_2_12_37_1","volume-title":"Gaussian Processes for Machine Learning","author":"Rasmussen C. E.","year":"2006"},{"key":"e_1_2_12_38_1","first-page":"133","article-title":"Introduction to Gaussian Processes","volume":"168","author":"MacKay D. J. C.","year":"1998","journal-title":"NATO ASI Series F Computer and Systems Sciences"},{"key":"e_1_2_12_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.125079"},{"key":"e_1_2_12_40_1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1318043"},{"key":"e_1_2_12_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110768"},{"key":"e_1_2_12_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2020.12.028"},{"key":"e_1_2_12_43_1","unstructured":"L.McClennyandU.Braga\u2010Neto \u201cSelf\u2010Adaptive Physics\u2010Informed Neural Networks Using a Soft Attention Mechanism \u201d2024 arXiv:2009.04544 http:\/\/arxiv.org\/abs\/2009.04544."},{"key":"e_1_2_12_44_1","unstructured":"S.Wang H.Wang J. H.Seidman andP.Perdikaris \u201cRandom Weight Factorization Improves the Training of Continuous Neural Representations \u201d2022."},{"key":"e_1_2_12_45_1","doi-asserted-by":"crossref","unstructured":"S.Wang S.Sankaran H.Wang andP.Perdikaris \u201cAn Expert's Guide to Training Physics\u2010Informed Neural Networks \u201d2023.","DOI":"10.1016\/j.cma.2024.116813"},{"key":"e_1_2_12_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"e_1_2_12_47_1","unstructured":"D. P.KingmaandJ.Ba \u201cAdam: A Method for Stochastic Optimization \u201d2017 https:\/\/arxiv.org\/abs\/1412.6980."},{"key":"e_1_2_12_48_1","doi-asserted-by":"publisher","DOI":"10.1088\/0266\u20105611\/30\/11\/114007"},{"key":"e_1_2_12_49_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467\u20109868.00294"},{"key":"e_1_2_12_50_1","doi-asserted-by":"publisher","DOI":"10.1113\/JP286193"},{"key":"e_1_2_12_51_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0886"},{"issue":"47","key":"e_1_2_12_52_1","first-page":"1593","article-title":"The No\u2010u\u2010Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo","volume":"15","author":"Hoffman M. D.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_12_53_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177011136"},{"key":"e_1_2_12_54_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10439\u2010015\u20101313\u20108"},{"key":"e_1_2_12_55_1","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00471.2010"},{"key":"e_1_2_12_56_1","doi-asserted-by":"publisher","DOI":"10.1161\/HYPERTENSIONAHA.110.167015"},{"key":"e_1_2_12_57_1","doi-asserted-by":"publisher","DOI":"10.3399\/bjgp11X593884"},{"key":"e_1_2_12_58_1","doi-asserted-by":"publisher","DOI":"10.7860\/JCDR\/2016\/14351.7458"},{"key":"e_1_2_12_59_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artmed.2024.102995"},{"key":"e_1_2_12_60_1","doi-asserted-by":"publisher","DOI":"10.3390\/biomedicines13092058"},{"key":"e_1_2_12_61_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2737"},{"key":"e_1_2_12_62_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssc.12374"},{"key":"e_1_2_12_63_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2025.110552"},{"key":"e_1_2_12_64_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2023.116351"},{"key":"e_1_2_12_65_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.115645"},{"key":"e_1_2_12_66_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2023.107676"},{"key":"e_1_2_12_67_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2024.0215"},{"key":"e_1_2_12_68_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.116846"},{"key":"e_1_2_12_69_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00162\u2010020\u201000530\u20102"},{"key":"e_1_2_12_70_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237\u2010016\u20100780\u20107"},{"key":"e_1_2_12_71_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112619"},{"key":"e_1_2_12_72_1","unstructured":"D.Lior C. G.Rusin J.Weigand et\u00a0al. \u201cDeformable Registration of Mra and 4D Flow Images to Facilitate Accurate Estimation of Flow Properties Within Blood Vessels \u201darXiv 2025 312 03116."},{"key":"e_1_2_12_73_1","doi-asserted-by":"publisher","DOI":"10.1038\/s42256\u2010021\u201000302\u20105"}],"container-title":["International Journal for Numerical Methods in Biomedical Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cnm.70147","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/cnm.70147","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cnm.70147","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cnm.70147","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T23:29:55Z","timestamp":1773012595000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cnm.70147"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2]]},"references-count":72,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.1002\/cnm.70147"],"URL":"https:\/\/doi.org\/10.1002\/cnm.70147","archive":["Portico"],"relation":{},"ISSN":["2040-7939","2040-7947"],"issn-type":[{"value":"2040-7939","type":"print"},{"value":"2040-7947","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2]]},"assertion":[{"value":"2025-09-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-18","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70147"}}