{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:40:22Z","timestamp":1740123622578,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T00:00:00Z","timestamp":1557964800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T00:00:00Z","timestamp":1557964800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["DMS-1719410","DMS-1719698"],"award-info":[{"award-number":["DMS-1719410","DMS-1719698"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-16-1-0103"],"award-info":[{"award-number":["W911NF-16-1-0103"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"crossref","award":["FA9550-18-1-0383"],"award-info":[{"award-number":["FA9550-18-1-0383"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s10915-019-00976-5","type":"journal-article","created":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T18:50:58Z","timestamp":1558032658000},"page":"1210-1239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise"],"prefix":"10.1007","volume":"81","author":[{"given":"Yong","family":"Liu","sequence":"first","affiliation":[]},{"given":"Tianheng","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7460-8313","authenticated-orcid":false,"given":"Yanlai","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,5,16]]},"reference":[{"key":"976_CR1","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.crma.2004.08.006","volume":"339","author":"M Barrault","year":"2004","unstructured":"Barrault, M., Nguyen, N.C., Maday, Y., Patera, A.T.: An \u201cempirical interpolation\u201d method: application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris 339, 667\u2013672 (2004)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"976_CR2","volume-title":"Generalized Inverses: Theory and Applications","author":"A Ben-Israel","year":"2003","unstructured":"Ben-Israel, A., Greville, T.N.: Generalized Inverses: Theory and Applications, vol. 15. Springer Science & Business Media, New York (2003)"},{"issue":"1","key":"976_CR3","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1146\/annurev.fl.25.010193.002543","volume":"25","author":"PHG Berkooz","year":"1993","unstructured":"Berkooz, P.H.G., Lumley, J.: The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 25(1), 539\u2013575 (1993)","journal-title":"Ann. Rev. Fluid Mech."},{"issue":"3","key":"976_CR4","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1051\/m2an\/2012045","volume":"47","author":"Haasdonk Bernard","year":"2013","unstructured":"Bernard, Haasdonk: Convergence rates of the pod-greedy method. ESAIM: Math. Model. Numer. Anal. 47(3), 859\u2013873 (2013)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"3","key":"976_CR5","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1137\/100795772","volume":"43","author":"P Binev","year":"2011","unstructured":"Binev, P., Cohen, A., Dahmen, W., Devore, R., Petrova, G., Wojtaszczyk, P.: Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43(3), 1457\u20131472 (2011)","journal-title":"SIAM J. Math. Anal."},{"key":"976_CR6","unstructured":"Boyd, J. P.: Chebyshev and Fourier spectral methods, Courier Corporation, (2001)"},{"issue":"2","key":"976_CR7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.2307\/1969178","volume":"48","author":"RH Cameron","year":"1947","unstructured":"Cameron, R.H., Martin, W.T.: The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Ann. Math. 48(2), 385\u2013392 (1947)","journal-title":"Ann. Math."},{"issue":"3","key":"976_CR8","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1007\/s10915-012-9654-z","volume":"55","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Gottlieb, S.: Reduced collocation methods: reduced basis methods in the collocation framework. J. Sci. Comput. 55(3), 718\u2013737 (2013)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"976_CR9","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1137\/09075250X","volume":"32","author":"Y Chen","year":"2010","unstructured":"Chen, Y., Hesthaven, J.S., Maday, Y., Rodr\u00edguez, J.: Certified reduced basis methods and output bounds for the harmonic maxwell\u2019s equations. SIAM J. Sci. Comput. 32(2), 970\u2013996 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"976_CR10","first-page":"1","volume":"7","author":"T Chen","year":"2019","unstructured":"Chen, T., Rozovskii, B., Shu, C.-W.: Numerical solutions of stochastic pdes driven by arbitrary type of noise. Stoch. Partial Diff. Equ. Anal. Comput. 7(1), 1\u201339 (2019)","journal-title":"Stoch. Partial Diff. Equ. Anal. Comput."},{"key":"976_CR11","doi-asserted-by":"publisher","first-page":"1963","DOI":"10.1016\/j.camwa.2018.11.032","volume":"77","author":"Y Chen","year":"2019","unstructured":"Chen, Y., Jiang, J., Narayan, A.: A robust error estimator and a residual-free error indicator for reduced basis methods. Comput. Math. Appl. 77, 1963\u20131979 (2019)","journal-title":"Comput. Math. Appl."},{"key":"976_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78572-9","volume-title":"Malliavin Calculus for L\u00e9vy Processes with Applications to Finance","author":"G Di Nunno","year":"2009","unstructured":"Di Nunno, G., \u00d8ksendal, B.K., Proske, F.: Malliavin Calculus for L\u00e9vy Processes with Applications to Finance, vol. 2. Springer, New York (2009)"},{"issue":"1","key":"976_CR13","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1137\/120881841","volume":"1","author":"H Elman","year":"2013","unstructured":"Elman, H., Liao, Q.: Reduced basis collocation methods for partial differential equations with random coefficients. SIAM\/ASA J. Uncertain. Quantif. 1(1), 192\u2013217 (2013)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"976_CR14","first-page":"1","volume-title":"Two Ways to Treat Time in Reduced Basis Methods","author":"S Glas","year":"2017","unstructured":"Glas, S., Mayerhofer, A., Urban, K.: Two Ways to Treat Time in Reduced Basis Methods, pp. 1\u201316. Springer International Publishing, Cham (2017)"},{"issue":"1","key":"976_CR15","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1051\/m2an:2005006","volume":"39","author":"MA Grepl","year":"2005","unstructured":"Grepl, M.A., Patera, A.T.: A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM: Math. Modell. Numer. Anal. 39(1), 157\u2013181 (2005)","journal-title":"ESAIM: Math. Modell. Numer. Anal."},{"key":"976_CR16","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/1.9781611974829.ch2","volume-title":"Model Reduction and Approximation","author":"Bernard Haasdonk","year":"2017","unstructured":"Haasdonk, B.: Chapter 2: Reduced Basis Methods for Parametrized PDEsNA Tutorial Introduction for Stationary and Instationary Problems, pp. 65\u2013136"},{"issue":"2","key":"976_CR17","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1051\/m2an:2008001","volume":"42","author":"B Haasdonk","year":"2008","unstructured":"Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Math. Model. Numer. Anal. 42(2), 277\u2013302 (2008)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"976_CR18","doi-asserted-by":"crossref","unstructured":"Hesthaven, J., Rozza, G., Stamm, B.: Certified Reduced Basis Methods for Parametrized Problems. Springer Briefs in Mathematics. Springer (2015)","DOI":"10.1007\/978-3-319-22470-1"},{"key":"976_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9215-6","volume-title":"Stochastic Partial Differential Equations","author":"H Holden","year":"1996","unstructured":"Holden, H., \u00d8ksendal, B., Ub\u00f8e, J., Zhang, T.: Stochastic Partial Differential Equations. Springer, New York (1996)"},{"issue":"2","key":"976_CR20","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/j.jcp.2006.01.008","volume":"216","author":"TY Hou","year":"2006","unstructured":"Hou, T.Y., Luo, W., Rozovskii, B., Zhou, H.-M.: Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. J. Comput. Phys. 216(2), 687\u2013706 (2006)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"976_CR21","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1007\/s10915-017-0551-3","volume":"73","author":"J Jiang","year":"2017","unstructured":"Jiang, J., Chen, Y., Narayan, A.: Offline-Enhanced reduced basis method through adaptive construction of the surrogate training set. J. Sci. Comput. 73(2), 853\u2013875 (2017)","journal-title":"J. Sci. Comput."},{"key":"976_CR22","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/978-3-540-30788-4_23","volume-title":"From Stochastic Calculus to Mathematical Finance","author":"Sergey Lototsky","year":"2006","unstructured":"Lototsky, S., Rozovskii, B.: Stochastic differential equations: a wiener chaos approach. In From Stochastic Calculus to Mathematical Finance, pp. 433\u2013506. Springer, Berlin (2006)"},{"issue":"2","key":"976_CR23","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1137\/S0363012993248918","volume":"35","author":"S Lototsky","year":"1997","unstructured":"Lototsky, S., Mikulevicius, R., Rozovskii, B.L.: Nonlinear filtering revisited: a spectral approach. SIAM J. Control Optim. 35(2), 435\u2013461 (1997)","journal-title":"SIAM J. Control Optim."},{"issue":"3\u20134","key":"976_CR24","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s00440-011-0384-1","volume":"154","author":"R Mikulevicius","year":"2012","unstructured":"Mikulevicius, R., Rozovskii, B.: On unbiased stochastic Navier\u2013Stokes equations. Probab. Theory Relat. Fields 154(3\u20134), 787\u2013834 (2012)","journal-title":"Probab. Theory Relat. Fields"},{"issue":"2","key":"976_CR25","first-page":"319","volume":"4","author":"R Mikulevicius","year":"2016","unstructured":"Mikulevicius, R., Rozovskii, B.: On distribution free Skorokhod\u2013Malliavin calculus. Stoch. Partial Diff. Equ. Anal. Comput. 4(2), 319\u2013360 (2016)","journal-title":"Stoch. Partial Diff. Equ. Anal. Comput."},{"issue":"1","key":"976_CR26","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1115\/1.1448332","volume":"124","author":"C Prud\u2019homme","year":"2002","unstructured":"Prud\u2019homme, C., Rovas, D., Veroy, K., Maday, Y., Patera, A.T., Turinici, G.: Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124(1), 70\u201380 (2002)","journal-title":"J. Fluids Eng."},{"key":"976_CR27","series-title":"UNITEXT","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15431-2","volume-title":"Reduced Basis Methods for Partial Differential Equations","author":"Alfio Quarteroni","year":"2016","unstructured":"Quarteroni, A., Manzoni, A., Negri, F.: Reduced Basis Methods for Partial Differential Equations. UNITEXT, vol. 92. Springer International Publishing, Cham (2016)"},{"issue":"3","key":"976_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF03024948","volume":"15","author":"G Rozza","year":"2007","unstructured":"Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15(3), 1 (2007)","journal-title":"Arch. Comput. Methods Eng."},{"issue":"3","key":"976_CR29","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s11831-008-9019-9","volume":"15","author":"G Rozza","year":"2008","unstructured":"Rozza, G., Huynh, D., Patera, A.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: application to transport and continuum mechanics. Arch. Comput. Methods Eng. 15(3), 229\u2013275 (2008)","journal-title":"Arch. Comput. Methods Eng."},{"issue":"288","key":"976_CR30","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1090\/S0025-5718-2013-02782-2","volume":"83","author":"K Urban","year":"2014","unstructured":"Urban, K., Patera, A.T.: An improved error bound for reduced basis approximation of linear parabolic problems. Math. Comput. 83(288), 1599\u20131615 (2014)","journal-title":"Math. Comput."},{"issue":"2","key":"976_CR31","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1103\/PhysRev.80.268","volume":"80","author":"G-C Wick","year":"1950","unstructured":"Wick, G.-C.: The evaluation of the collision matrix. Phys. Rev. 80(2), 268 (1950)","journal-title":"Phys. Rev."},{"issue":"11","key":"976_CR32","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.2514\/2.1570","volume":"40","author":"K Willcox","year":"2002","unstructured":"Willcox, K., Peraire, J.: Balanced model reduction via the proper orthogonal decomposition. AIAA J. 40(11), 2323\u20132330 (2002)","journal-title":"AIAA J."},{"key":"976_CR33","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctv7h0skv","volume-title":"Numerical Methods for Stochastic Computations: A Spectral Method Approach","author":"D Xiu","year":"2010","unstructured":"Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton (2010)"},{"issue":"2","key":"976_CR34","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1137\/S1064827501387826","volume":"24","author":"D Xiu","year":"2002","unstructured":"Xiu, D., Karniadakis, G.E.: The Wiener\u2013Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619\u2013644 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"09","key":"976_CR35","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1142\/S0218202514500110","volume":"24","author":"M Yano","year":"2014","unstructured":"Yano, M., Patera, A.T., Urban, K.: A space-time hp-interpolation-based certified reduced basis method for burgers\u2019 equation. Math. Models Methods Appl. Sci. 24(09), 1903\u20131935 (2014)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"2","key":"976_CR36","doi-asserted-by":"publisher","first-page":"A914","DOI":"10.1137\/110849572","volume":"34","author":"Z Zhang","year":"2012","unstructured":"Zhang, Z., Rozovskii, B., Tretyakov, M.V., Karniadakis, G.E.: A multistage wiener chaos expansion method for stochastic advection\u2013diffusion\u2013reaction equations. SIAM J. Sci. Comput. 34(2), A914\u2013A936 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"976_CR37","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1137\/130932156","volume":"53","author":"Z Zhang","year":"2015","unstructured":"Zhang, Z., Tretyakov, M.V., Rozovskii, B., Karniadakis, G.E.: Wiener chaos versus stochastic collocation methods for linear advection\u2013diffusion\u2013reaction equations with multiplicative white noise. SIAM J. Numer. Anal. 53(1), 153\u2013183 (2015)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00976-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-019-00976-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00976-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:43:59Z","timestamp":1589708639000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-019-00976-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,16]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["976"],"URL":"https:\/\/doi.org\/10.1007\/s10915-019-00976-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2019,5,16]]},"assertion":[{"value":"2 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}