{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T15:31:04Z","timestamp":1783697464051,"version":"3.55.0"},"reference-count":227,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T00:00:00Z","timestamp":1654732800000},"content-version":"unspecified","delay-in-days":39,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acta Numerica"],"published-print":{"date-parts":[[2022,5]]},"abstract":"<jats:p>Numerical simulation of parametrized differential equations is of crucial importance in the study of real-world phenomena in applied science and engineering. Computational methods for real-time and many-query simulation of such problems often require prohibitively high computational costs to achieve sufficiently accurate numerical solutions. During the last few decades, model order reduction has proved successful in providing low-complexity high-fidelity surrogate models that allow rapid and accurate simulations under parameter variation, thus enabling the numerical simulation of increasingly complex problems. However, many challenges remain to secure the robustness and efficiency needed for the numerical simulation of nonlinear time-dependent problems. The purpose of this article is to survey the state of the art of reduced basis methods for time-dependent problems and draw together recent advances in three main directions. First, we discuss structure-preserving reduced order models designed to retain key physical properties of the continuous problem. Second, we survey localized and adaptive methods based on nonlinear approximations of the solution space. Finally, we consider data-driven techniques based on non-intrusive reduced order models in which an approximation of the map between parameter space and coefficients of the reduced basis is learned. Within each class of methods, we describe different approaches and provide a comparative discussion that lends insights to advantages, disadvantages and potential open questions.<\/jats:p>","DOI":"10.1017\/s0962492922000058","type":"journal-article","created":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T11:15:48Z","timestamp":1654773348000},"page":"265-345","source":"Crossref","is-referenced-by-count":90,"title":["Reduced basis methods for time-dependent problems"],"prefix":"10.1017","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8074-1586","authenticated-orcid":false,"given":"Jan S.","family":"Hesthaven","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cecilia","family":"Pagliantini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2022,6,9]]},"reference":[{"key":"S0962492922000058_r21","doi-asserted-by":"publisher","DOI":"10.1137\/030600515"},{"key":"S0962492922000058_r70","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.114181"},{"key":"S0962492922000058_r79","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2007031"},{"key":"S0962492922000058_r102","doi-asserted-by":"publisher","DOI":"10.3182\/20130904-3-FR-2041.00160"},{"key":"S0962492922000058_r185","first-page":"851","volume-title":"ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences","author":"Rozza","year":"2009"},{"key":"S0962492922000058_r126","volume-title":"Probability Theory: Foundations","author":"Lo\u00e8ve","year":"1955"},{"key":"S0962492922000058_r76","volume-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"key":"S0962492922000058_r184","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-008-9019-9"},{"key":"S0962492922000058_r207","first-page":"1339","volume-title":"Port-Hamiltonian systems: An introductory survey, in International Congress of Mathematicians 2006","author":"van der Schaft","year":"2006"},{"key":"S0962492922000058_r223","doi-asserted-by":"publisher","DOI":"10.1137\/18M1221837"},{"key":"S0962492922000058_r24","doi-asserted-by":"publisher","DOI":"10.1002\/nme.5499"},{"key":"S0962492922000058_r142","doi-asserted-by":"publisher","DOI":"10.1137\/140967787"},{"key":"S0962492922000058_r15","unstructured":"Beattie, C. , Gugercin, S. and Mehrmann, V. (2019), Structure-preserving interpolatory model reduction for port-Hamiltonian differential-algebraic systems. Available at arXiv:1910.05674. To appear in a Festschrift to honour the 70th birthday of A. Antoulas."},{"key":"S0962492922000058_r198","doi-asserted-by":"publisher","DOI":"10.1007\/s00162-019-00494-y"},{"key":"S0962492922000058_r212","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2015.08.104"},{"key":"S0962492922000058_r137","doi-asserted-by":"publisher","DOI":"10.1007\/s13160-019-00378-y"},{"key":"S0962492922000058_r36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.05.019"},{"key":"S0962492922000058_r209","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.04.025"},{"key":"S0962492922000058_r117","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00227-6"},{"key":"S0962492922000058_r172","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"S0962492922000058_r144","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.12.035"},{"key":"S0962492922000058_r147","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7949(81)90106-1"},{"key":"S0962492922000058_r216","doi-asserted-by":"publisher","DOI":"10.2514\/2.1570"},{"key":"S0962492922000058_r189","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-005-0963-2"},{"key":"S0962492922000058_r5","first-page":"1","volume-title":"Finite element exterior calculus, homological techniques, and applications, in Acta Numerica","volume":"15","author":"Arnold","year":"2006"},{"key":"S0962492922000058_r100","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2011.02.003"},{"key":"S0962492922000058_r125","doi-asserted-by":"publisher","DOI":"10.1137\/090775622"},{"key":"S0962492922000058_r14","doi-asserted-by":"crossref","unstructured":"Beattie, C. and Gugercin, S. (2011), Structure-preserving model reduction for nonlinear port-Hamiltonian systems, in 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp. 6564\u20136569.","DOI":"10.1109\/CDC.2011.6161504"},{"key":"S0962492922000058_r143","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0745-0_2"},{"key":"S0962492922000058_r197","doi-asserted-by":"publisher","DOI":"10.1007\/s00348-012-1354-9"},{"key":"S0962492922000058_r166","first-page":"665","article-title":"Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity, Automatica","volume":"46","author":"Polyuga","year":"2010","journal-title":"J. IFAC"},{"key":"S0962492922000058_r65","doi-asserted-by":"publisher","DOI":"10.1137\/16M1095202"},{"key":"S0962492922000058_r20","unstructured":"Berzins, A. , Helmig, J. , Key, F. and Elgeti, S. (2020), Standardized non-intrusive reduced order modeling using different regression models with application to complex flow problems. Available at arXiv:2006.13706."},{"key":"S0962492922000058_r111","doi-asserted-by":"publisher","DOI":"10.2514\/1.J057791"},{"key":"S0962492922000058_r6","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8928(66)90070-0"},{"key":"S0962492922000058_r130","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-48721-8_4"},{"key":"S0962492922000058_r133","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21792-5"},{"key":"S0962492922000058_r138","unstructured":"Mojgani, R. and Balajewicz, M. (2017), Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows. Available at arXiv:1701.04343."},{"key":"S0962492922000058_r205","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2021.03.042"},{"key":"S0962492922000058_r154","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-021-01211-w"},{"key":"S0962492922000058_r164","doi-asserted-by":"publisher","DOI":"10.1137\/0910047"},{"key":"S0962492922000058_r13","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2008.10.016"},{"key":"S0962492922000058_r120","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.108973"},{"key":"S0962492922000058_r87","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2008001"},{"key":"S0962492922000058_r169","doi-asserted-by":"publisher","DOI":"10.1115\/1.1448332"},{"key":"S0962492922000058_r165","unstructured":"Pichi, F. , Ballarin, F. , Rozza, G. and Hesthaven, J. S. (2021), An artificial neural network approach to bifurcating phenomena in computational fluid dynamics. Available at arXiv:2109.10765."},{"key":"S0962492922000058_r122","doi-asserted-by":"crossref","unstructured":"LeGresley, P. A. and Alonso, J. J. (2000), Airfoil design optimization using reduced order models based on proper orthogonal decomposition, in Fluids 2000 Conference and Exhibit. AIAA paper 2000-2545.","DOI":"10.2514\/6.2000-2545"},{"key":"S0962492922000058_r55","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974829.ch3"},{"key":"S0962492922000058_r63","doi-asserted-by":"crossref","unstructured":"Eldred, M. and Dunlavy, D. (2006), Formulations for surrogate-based optimization with data fit, multifidelity, and reduced-order models, in 11th AIAA\/ISSMO Multidisciplinary Analysis and Optimization Conference, pp. 1\u201320. AIAA paper 2006-7117.","DOI":"10.2514\/6.2006-7117"},{"key":"S0962492922000058_r167","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2128650"},{"key":"S0962492922000058_r95","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2013100"},{"key":"S0962492922000058_r183","first-page":"153","volume-title":"Separated Representation and PGD Based Model Reduction: Fundamentals and Applications","volume":"554","author":"Rozza","year":"2014"},{"key":"S0962492922000058_r116","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2006.184"},{"key":"S0962492922000058_r112","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900382612"},{"key":"S0962492922000058_r46","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598333181"},{"key":"S0962492922000058_r56","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-013-9186-2"},{"key":"S0962492922000058_r171","doi-asserted-by":"publisher","DOI":"10.1186\/2190-5983-1-3"},{"key":"S0962492922000058_r16","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(99)00047-2"},{"key":"S0962492922000058_r25","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2020057"},{"key":"S0962492922000058_r141","unstructured":"Musharbash, E. and Nobile, F. (2017), Symplectic dynamical low rank approximation of wave equations with random parameters. Technical report 18.2017, EPFL-SB-Institute of Mathematics-Mathicse."},{"key":"S0962492922000058_r91","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3618"},{"key":"S0962492922000058_r81","volume-title":"Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms","author":"Gunzburger","year":"1989"},{"key":"S0962492922000058_r99","first-page":"417","volume":"24","author":"Hotelling","year":"1933","journal-title":"Analysis of a complex of statistical variables into principal components"},{"key":"S0962492922000058_r69","doi-asserted-by":"publisher","DOI":"10.2514\/3.6141"},{"key":"S0962492922000058_r31","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500018411"},{"key":"S0962492922000058_r180","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(00)00042-7"},{"key":"S0962492922000058_r106","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-018-9593-9"},{"key":"S0962492922000058_r39","doi-asserted-by":"publisher","DOI":"10.1137\/140959602"},{"key":"S0962492922000058_r134","first-page":"289","article-title":"Hamiltonian systems with symmetry, coadjoint orbits and plasma physics","volume":"117","author":"Marsden","year":"1983","journal-title":"Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur."},{"key":"S0962492922000058_r48","unstructured":"CISCO (2019), Cisco visual networking index: Global mobile data traffic forecast update, 2017\u20132022."},{"key":"S0962492922000058_r101","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.89.022923"},{"key":"S0962492922000058_r192","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3093-4"},{"key":"S0962492922000058_r182","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2004.11.004"},{"key":"S0962492922000058_r60","doi-asserted-by":"publisher","DOI":"10.2514\/1.J056405"},{"key":"S0962492922000058_r219","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4066"},{"key":"S0962492922000058_r135","first-page":"52","volume-title":"Artificial Neural Networks and Machine Learning","author":"Masci","year":"2011"},{"key":"S0962492922000058_r187","doi-asserted-by":"publisher","DOI":"10.1038\/323533a0"},{"key":"S0962492922000058_r175","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78841-6_7"},{"key":"S0962492922000058_r195","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112010001217"},{"key":"S0962492922000058_r146","first-page":"235","article-title":"Invariante variationsprobleme","volume":"1918","author":"Noether","year":"1918","journal-title":"Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen, Mathematisch-Physikalische Klasse"},{"key":"S0962492922000058_r227","doi-asserted-by":"publisher","DOI":"10.1002\/nme.5610"},{"key":"S0962492922000058_r3","article-title":"PEBL-ROM: Projection-error based local reduced-order models","volume":"3","author":"Amsallem","year":"2016","journal-title":"Adv. Model. Simul. Engrg Sci."},{"key":"S0962492922000058_r29","first-page":"43","article-title":"Symplectic model order reduction with non-orthonormal bases","volume":"24","author":"Buchfink","year":"2019","journal-title":"Math. Comput. Appl."},{"key":"S0962492922000058_r74","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.01.047"},{"key":"S0962492922000058_r50","doi-asserted-by":"publisher","DOI":"10.1002\/fld.3946"},{"key":"S0962492922000058_r186","unstructured":"Rozza, G. , Malik, H. , Demo, N. , Tezzele, M. , Girfoglio, M. , Stabile, G. and Mola, A. (2018), Advances in reduced order methods for parametric industrial problems in computational fluid dynamics, in ECCOMAS ECFD 7: Proceedings of 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7) ( Owen, R. et al., eds), pp. 59\u201376."},{"key":"S0962492922000058_r201","doi-asserted-by":"publisher","DOI":"10.1137\/19M1271270"},{"key":"S0962492922000058_r22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.112896"},{"key":"S0962492922000058_r132","doi-asserted-by":"publisher","DOI":"10.1137\/120873868"},{"key":"S0962492922000058_r32","doi-asserted-by":"crossref","unstructured":"Bui-Thanh, T. , Damodaran, M. and Willcox, K. (2003), Proper orthogonal decomposition extensions for parametric applications in compressible aerodynamics, in 21st Applied Aerodynamics Conference. AIAA paper 2003-4213.","DOI":"10.2514\/6.2003-4213"},{"key":"S0962492922000058_r163","doi-asserted-by":"publisher","DOI":"10.1137\/140978922"},{"key":"S0962492922000058_r222","doi-asserted-by":"publisher","DOI":"10.1177\/0954410019890721"},{"key":"S0962492922000058_r75","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.11.016"},{"key":"S0962492922000058_r17","volume-title":"Advances in Neural Information Processing Systems","volume":"14","author":"Belkin","year":"2001"},{"key":"S0962492922000058_r224","doi-asserted-by":"publisher","DOI":"10.3390\/fluids6080296"},{"key":"S0962492922000058_r26","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.07.021"},{"key":"S0962492922000058_r159","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.03.025"},{"key":"S0962492922000058_r113","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-021-09551-4"},{"key":"S0962492922000058_r105","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1904-8"},{"key":"S0962492922000058_r128","doi-asserted-by":"publisher","DOI":"10.1137\/17M1111991"},{"key":"S0962492922000058_r89","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","volume":"31","author":"Hairer","year":"2006"},{"key":"S0962492922000058_r61","doi-asserted-by":"publisher","DOI":"10.1137\/090780122"},{"key":"S0962492922000058_r54","doi-asserted-by":"publisher","DOI":"10.1016\/j.crme.2019.11.012"},{"key":"S0962492922000058_r226","doi-asserted-by":"publisher","DOI":"10.1137\/17M1123286"},{"key":"S0962492922000058_r181","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/4\/304"},{"key":"S0962492922000058_r45","doi-asserted-by":"publisher","DOI":"10.1137\/09075250X"},{"key":"S0962492922000058_r38","unstructured":"Carlberg, K. , Guzzetti, S. , Khalil, M. and Sargsyan, K. (2019), The network uncertainty quantification method for propagating uncertainties in component-based systems. Available at arXiv:1908.11476."},{"key":"S0962492922000058_r9","volume-title":"Analytics in a Big Data World: The Essential Guide to Data Science and its Applications","author":"Baesens","year":"2014"},{"key":"S0962492922000058_r176","doi-asserted-by":"publisher","DOI":"10.1137\/17M1140571"},{"key":"S0962492922000058_r4","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4371"},{"key":"S0962492922000058_r225","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502419154"},{"key":"S0962492922000058_r19","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"S0962492922000058_r34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-78325-3_10"},{"key":"S0962492922000058_r173","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"S0962492922000058_r66","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-007-9321-1"},{"key":"S0962492922000058_r107","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6751"},{"key":"S0962492922000058_r119","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00485-X"},{"key":"S0962492922000058_r28","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113"},{"key":"S0962492922000058_r200","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06260-0_12"},{"key":"S0962492922000058_r190","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1969.222678"},{"key":"S0962492922000058_r208","doi-asserted-by":"crossref","unstructured":"Veroy, K. , Prud\u2019homme, C. , Rovas, D. V. and Patera, A. T. (2003), A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, in Proceedings of the 16th AIAA Computational Fluid Dynamics Conference. AIAA paper 2003-3847.","DOI":"10.2514\/6.2003-3847"},{"key":"S0962492922000058_r92","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.02.037"},{"key":"S0962492922000058_r96","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109513"},{"key":"S0962492922000058_r129","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-018-0653-6"},{"key":"S0962492922000058_r193","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.09.017"},{"key":"S0962492922000058_r94","volume-title":"Certified Reduced Basis Methods for Parametrized Partial Differential Equations","author":"Hesthaven","year":"2015"},{"key":"S0962492922000058_r104","first-page":"215","volume-title":"Acta Numerica","volume":"9","author":"Iserles","year":"2000"},{"key":"S0962492922000058_r215","doi-asserted-by":"publisher","DOI":"10.1137\/16M1059904"},{"key":"S0962492922000058_r153","first-page":"1","article-title":"A Gaussian process regression approach within a data-driven POD framework for engineering problems in fluid dynamics","volume":"4","author":"Ortali","year":"2022","journal-title":"Math. Engrg"},{"key":"S0962492922000058_r51","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-3286-8_76"},{"key":"S0962492922000058_r124","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475035"},{"key":"S0962492922000058_r206","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"van der Maaten","year":"2008","journal-title":"J. Mach. Learning Res."},{"key":"S0962492922000058_r44","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2009037"},{"key":"S0962492922000058_r151","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.4.093902"},{"key":"S0962492922000058_r52","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"S0962492922000058_r35","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4800"},{"key":"S0962492922000058_r42","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-012-9130-9"},{"key":"S0962492922000058_r123","volume-title":"Simulating Hamiltonian Dynamics","volume":"14","author":"Leimkuhler","year":"2004"},{"key":"S0962492922000058_r68","doi-asserted-by":"publisher","DOI":"10.1007\/BF01391412"},{"key":"S0962492922000058_r11","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2010.12.015"},{"key":"S0962492922000058_r131","volume-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"MacQueen","year":"1967"},{"key":"S0962492922000058_r67","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19830630105"},{"key":"S0962492922000058_r8","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2540"},{"key":"S0962492922000058_r30","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2011056"},{"key":"S0962492922000058_r49","volume-title":"Active subspace methods in theory and practice: Applications to kriging surfaces","author":"Constantine","year":"2014"},{"key":"S0962492922000058_r86","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2012045"},{"key":"S0962492922000058_r140","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(80)90776-8"},{"key":"S0962492922000058_r178","doi-asserted-by":"publisher","DOI":"10.1137\/17M1113679"},{"key":"S0962492922000058_r152","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2013.10.028"},{"key":"S0962492922000058_r211","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109402"},{"key":"S0962492922000058_r115","doi-asserted-by":"publisher","DOI":"10.1137\/15M1023543"},{"key":"S0962492922000058_r199","volume-title":"Conservative Finite-Difference Methods on General Grids","author":"Shashkov","year":"1996"},{"key":"S0962492922000058_r149","doi-asserted-by":"publisher","DOI":"10.2514\/3.50778"},{"key":"S0962492922000058_r188","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2406"},{"key":"S0962492922000058_r191","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109736"},{"key":"S0962492922000058_r40","doi-asserted-by":"publisher","DOI":"10.1137\/090766498"},{"key":"S0962492922000058_r156","volume-title":"Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations","author":"Patera","year":"2007"},{"key":"S0962492922000058_r78","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2005006"},{"key":"S0962492922000058_r88","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2011.547674"},{"key":"S0962492922000058_r118","doi-asserted-by":"publisher","DOI":"10.3138\/9781487583057"},{"key":"S0962492922000058_r145","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-009-0005-x"},{"key":"S0962492922000058_r168","doi-asserted-by":"publisher","DOI":"10.1137\/0724083"},{"key":"S0962492922000058_r160","doi-asserted-by":"publisher","DOI":"10.1186\/s40323-016-0064-x"},{"key":"S0962492922000058_r7","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2006102"},{"key":"S0962492922000058_r23","doi-asserted-by":"publisher","DOI":"10.1137\/100795772"},{"key":"S0962492922000058_r196","first-page":"583","volume-title":"Artificial Neural Networks (ICANN\u201997)","author":"Sch\u00f6lkopf","year":"1997"},{"key":"S0962492922000058_r220","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(03)00370-7"},{"key":"S0962492922000058_r109","doi-asserted-by":"publisher","DOI":"10.1137\/050639703"},{"key":"S0962492922000058_r204","first-page":"569","volume-title":"Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research","author":"Tezzele","year":"2018b"},{"key":"S0962492922000058_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.02.028"},{"key":"S0962492922000058_r33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.10.026"},{"key":"S0962492922000058_r59","doi-asserted-by":"publisher","DOI":"10.1063\/5.0031142"},{"key":"S0962492922000058_r179","doi-asserted-by":"publisher","DOI":"10.1037\/h0042519"},{"key":"S0962492922000058_r210","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.01.031"},{"key":"S0962492922000058_r202","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2319"},{"key":"S0962492922000058_r18","doi-asserted-by":"publisher","DOI":"10.1137\/110836742"},{"key":"S0962492922000058_r84","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2018.10.029"},{"key":"S0962492922000058_r203","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-96649-6_8"},{"key":"S0962492922000058_r58","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100016108"},{"key":"S0962492922000058_r27","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-fluid-010719-060214"},{"key":"S0962492922000058_r12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2100"},{"key":"S0962492922000058_r214","first-page":"106","volume-title":"Proceedings of the Twenty-First International Conference on Machine Learning (ICML \u201904)","author":"Weinberger","year":"2004"},{"key":"S0962492922000058_r108","first-page":"79","article-title":"\u00dcber lineare Methoden in der Wahrscheinlichkeitsrechnung","volume":"1947","author":"Karhunen","year":"1947","journal-title":"Ann. Acad. Sci. Fenn. Ser. A. I. Math.-Phys."},{"key":"S0962492922000058_r161","doi-asserted-by":"publisher","DOI":"10.1137\/130924408"},{"key":"S0962492922000058_r98","first-page":"237","volume-title":"Acta Numerica","volume":"11","author":"Hiptmair","year":"2002"},{"key":"S0962492922000058_r157","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2015.03.018"},{"key":"S0962492922000058_r71","first-page":"267","volume-title":"Acta Numerica","volume":"12","author":"Freund","year":"2003"},{"key":"S0962492922000058_r155","doi-asserted-by":"publisher","DOI":"10.2514\/1.C032062"},{"key":"S0962492922000058_r218","doi-asserted-by":"publisher","DOI":"10.3166\/ejc.16.401-406"},{"key":"S0962492922000058_r139","doi-asserted-by":"publisher","DOI":"10.1016\/j.crme.2019.11.009"},{"key":"S0962492922000058_r41","doi-asserted-by":"publisher","DOI":"10.1137\/15M1055085"},{"key":"S0962492922000058_r121","doi-asserted-by":"publisher","DOI":"10.1007\/s00348-017-2456-1"},{"key":"S0962492922000058_r177","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2002.806601"},{"key":"S0962492922000058_r47","first-page":"1","volume-title":"Acta Numerica","volume":"20","author":"Christiansen","year":"2011"},{"key":"S0962492922000058_r97","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-015-9420-5"},{"key":"S0962492922000058_r53","first-page":"14","article-title":"Sur le probl\u00e8me de Pfaff","volume":"6","author":"Darboux","year":"1882","journal-title":"Bulletin des Sciences Math\u00e9matiques et Astronomiques"},{"key":"S0962492922000058_r213","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-008-0309-5"},{"key":"S0962492922000058_r62","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2020013"},{"key":"S0962492922000058_r103","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2010.01.003"},{"key":"S0962492922000058_r77","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2017.0385"},{"key":"S0962492922000058_r221","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202514500110"},{"key":"S0962492922000058_r158","doi-asserted-by":"publisher","DOI":"10.1137\/140989169"},{"key":"S0962492922000058_r93","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2022013"},{"key":"S0962492922000058_r80","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.052"},{"key":"S0962492922000058_r170","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15431-2"},{"key":"S0962492922000058_r10","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.006"},{"key":"S0962492922000058_r90","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.03.050"},{"key":"S0962492922000058_r148","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(82)90096-2"},{"key":"S0962492922000058_r217","doi-asserted-by":"publisher","DOI":"10.1137\/120899042"},{"key":"S0962492922000058_r57","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2009.2021005"},{"key":"S0962492922000058_r127","doi-asserted-by":"publisher","DOI":"10.4171\/067"},{"key":"S0962492922000058_r150","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620200711"},{"key":"S0962492922000058_r174","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0363(20001115)34:5<425::AID-FLD67>3.0.CO;2-W"},{"key":"S0962492922000058_r72","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.07.008"},{"key":"S0962492922000058_r83","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2018.07.017"},{"key":"S0962492922000058_r43","doi-asserted-by":"publisher","DOI":"10.2514\/1.J056161"},{"key":"S0962492922000058_r162","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7799422"},{"key":"S0962492922000058_r136","doi-asserted-by":"publisher","DOI":"10.1063\/1.1664701"},{"key":"S0962492922000058_r2","doi-asserted-by":"publisher","DOI":"10.2514\/3.7539"},{"key":"S0962492922000058_r85","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2020.1004"},{"key":"S0962492922000058_r1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0061577"},{"key":"S0962492922000058_r73","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2020-0064"},{"key":"S0962492922000058_r110","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(79)90057-4"},{"key":"S0962492922000058_r194","doi-asserted-by":"publisher","DOI":"10.1002\/nme.6667"},{"key":"S0962492922000058_r82","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.08.004"},{"key":"S0962492922000058_r114","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974508"},{"key":"S0962492922000058_r64","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4820"}],"container-title":["Acta Numerica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0962492922000058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T11:19:11Z","timestamp":1654773551000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0962492922000058\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5]]},"references-count":227,"alternative-id":["S0962492922000058"],"URL":"https:\/\/doi.org\/10.1017\/s0962492922000058","relation":{},"ISSN":["0962-4929","1474-0508"],"issn-type":[{"value":"0962-4929","type":"print"},{"value":"1474-0508","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5]]}}}