He, QiZhi; Perego, Mauro; Howard, Amanda A.; Karniadakis, George Em; Stinis, Panos A hybrid deep neural operator/finite element method for ice-sheet modeling. (English) Zbl 07742911 J. Comput. Phys. 492, Article ID 112428, 17 p. (2023). MSC: 86Axx 76Mxx 65Cxx PDFBibTeX XMLCite \textit{Q. He} et al., J. Comput. Phys. 492, Article ID 112428, 17 p. (2023; Zbl 07742911) Full Text: DOI arXiv
Deng, Mingge; Tushar, Faisal; Bravo, Luis; Ghoshal, Anindya; Karniadakis, George; Li, Zhen Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale. (English) Zbl 1512.76133 J. Fluid Mech. 942, Paper No. A29, 22 p. (2022). MSC: 76W05 76T20 76M35 PDFBibTeX XMLCite \textit{M. Deng} et al., J. Fluid Mech. 942, Paper No. A29, 22 p. (2022; Zbl 1512.76133) Full Text: DOI arXiv
Meng, Xuhui; Babaee, Hessam; Karniadakis, George Em Multi-fidelity Bayesian neural networks: algorithms and applications. (English) Zbl 07505956 J. Comput. Phys. 438, Article ID 110361, 16 p. (2021). MSC: 68Txx 65Cxx 76-XX PDFBibTeX XMLCite \textit{X. Meng} et al., J. Comput. Phys. 438, Article ID 110361, 16 p. (2021; Zbl 07505956) Full Text: DOI arXiv
Cho, Heyrim; Venturi, Daniele; Karniadakis, George Em Numerical methods for high-dimensional kinetic equations. (English) Zbl 1404.65117 Jin, Shi (ed.) et al., Uncertainty quantification for hyperbolic and kinetic equations. Cham: Springer (ISBN 978-3-319-67109-3/hbk; 978-3-319-67110-9/ebook). SEMA SIMAI Springer Series 14, 93-125 (2017). MSC: 65M12 35R60 76P05 82C31 65M50 65M06 65D32 65M55 15A69 41A63 65M70 65M60 65L05 PDFBibTeX XMLCite \textit{H. Cho} et al., SEMA SIMAI Springer Ser. 14, 93--125 (2017; Zbl 1404.65117) Full Text: DOI
Li, Z.; Bian, X.; Li, X.; Deng, M.; Tang, Y.-H.; Caswell, B.; Karniadakis, George E. Dissipative particle dynamics: foundation, evolution, implementation, and applications. (English) Zbl 1387.35496 Bodnár, Tomáš (ed.) et al., Particles in flows. Based on the summer course and workshop, Prague, Czech Republic, August 2014. Cham: Birkhäuser/Springer (ISBN 978-3-319-60281-3/hbk; 978-3-319-60282-0/ebook). Advances in Mathematical Fluid Mechanics, 255-326 (2017). MSC: 35Q35 76Z05 76V05 74F10 80A32 92C35 74F25 80A30 92C45 92C40 35Q84 82C31 60H15 82C40 PDFBibTeX XMLCite \textit{Z. Li} et al., in: Particles in flows. Based on the summer course and workshop, Prague, Czech Republic, August 2014. Cham: Birkhäuser/Springer. 255--326 (2017; Zbl 1387.35496) Full Text: DOI
Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems. (English) Zbl 1380.76093 J. Comput. Phys. 344, 303-319 (2017). MSC: 76M25 35A35 35R60 76D06 35Q35 PDFBibTeX XMLCite \textit{H. Babaee} et al., J. Comput. Phys. 344, 303--319 (2017; Zbl 1380.76093) Full Text: DOI
Cho, H.; Venturi, D.; Karniadakis, G. E. Numerical methods for high-dimensional probability density function equations. (English) Zbl 1349.65046 J. Comput. Phys. 305, 817-837 (2016). MSC: 65C50 60H35 35Q20 35Q82 35Q84 62J10 65M75 PDFBibTeX XMLCite \textit{H. Cho} et al., J. Comput. Phys. 305, 817--837 (2016; Zbl 1349.65046) Full Text: DOI Link
Kim, Changho; Borodin, Oleg; Karniadakis, George Em Quantification of sampling uncertainty for molecular dynamics simulation: time-dependent diffusion coefficient in simple fluids. (English) Zbl 1349.76762 J. Comput. Phys. 302, 485-508 (2015). MSC: 76M35 65M32 76R50 PDFBibTeX XMLCite \textit{C. Kim} et al., J. Comput. Phys. 302, 485--508 (2015; Zbl 1349.76762) Full Text: DOI
Kim, Changho; Karniadakis, George Em Brownian motion of a Rayleigh particle confined in a channel: a generalized Langevin equation approach. (English) Zbl 1317.82043 J. Stat. Phys. 158, No. 5, 1100-1125 (2015). MSC: 82C31 60J65 60J60 PDFBibTeX XMLCite \textit{C. Kim} and \textit{G. E. Karniadakis}, J. Stat. Phys. 158, No. 5, 1100--1125 (2015; Zbl 1317.82043) Full Text: DOI
Venturi, D.; Karniadakis, G. E. Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems. (English) Zbl 1371.60119 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 470, No. 2166, Article ID 20130754, 20 p. (2014). MSC: 60H30 82B05 PDFBibTeX XMLCite \textit{D. Venturi} and \textit{G. E. Karniadakis}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 470, No. 2166, Article ID 20130754, 20 p. (2014; Zbl 1371.60119) Full Text: DOI
Kim, Changho; Karniadakis, George Em Time correlation functions of Brownian motion and evaluation of friction coefficient in the near-Brownian-limit regime. (English) Zbl 1327.82067 Multiscale Model. Simul. 12, No. 1, 225-248 (2014). Reviewer: Bassano Vacchini (Milano) MSC: 82C31 82D05 37M05 60J65 PDFBibTeX XMLCite \textit{C. Kim} and \textit{G. E. Karniadakis}, Multiscale Model. Simul. 12, No. 1, 225--248 (2014; Zbl 1327.82067) Full Text: DOI Link
Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em A convergence study for SPDEs using combined polynomial chaos and dynamically-orthogonal schemes. (English) Zbl 1349.65509 J. Comput. Phys. 245, 281-301 (2013). MSC: 65M70 65M75 82C22 60H15 60H35 PDFBibTeX XMLCite \textit{M. Choi} et al., J. Comput. Phys. 245, 281--301 (2013; Zbl 1349.65509) Full Text: DOI
Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. (English) Zbl 1408.76428 J. Comput. Phys. 231, No. 4, 1587-1614 (2012). MSC: 76M35 65C05 76J20 76R99 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Comput. Phys. 231, No. 4, 1587--1614 (2012; Zbl 1408.76428) Full Text: DOI
Venturi, Daniele; Wan, Xiaoliang; Karniadakis, George Em Stochastic bifurcation analysis of Rayleigh-Bénard convection. (English) Zbl 1189.76213 J. Fluid Mech. 650, 391-413 (2010). MSC: 76E06 76M35 76R10 80A20 PDFBibTeX XMLCite \textit{D. Venturi} et al., J. Fluid Mech. 650, 391--413 (2010; Zbl 1189.76213) Full Text: DOI
Lin, Guang; Karniadakis, G. E. Sensitivity analysis and stochastic simulations of non-equilibrium plasma flow. (English) Zbl 1176.76109 Int. J. Numer. Methods Eng. 80, No. 6-7, 738-766 (2009). MSC: 76M35 76X05 PDFBibTeX XMLCite \textit{G. Lin} and \textit{G. E. Karniadakis}, Int. J. Numer. Methods Eng. 80, No. 6--7, 738--766 (2009; Zbl 1176.76109) Full Text: DOI
Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. Stochastic modeling of random roughness in shock scattering problems: theory and simulations. (English) Zbl 1194.76099 Comput. Methods Appl. Mech. Eng. 197, No. 43-44, 3420-3434 (2008). MSC: 76L05 76M35 PDFBibTeX XMLCite \textit{G. Lin} et al., Comput. Methods Appl. Mech. Eng. 197, No. 43--44, 3420--3434 (2008; Zbl 1194.76099) Full Text: DOI
Venturi, Daniele; Wan, Xiaoliang; Karniadakis, George Em Stochastic low-dimensional modelling of a random laminar wake past a circular cylinder. (English) Zbl 1146.76018 J. Fluid Mech. 606, 339-367 (2008). MSC: 76D25 76M35 76D06 PDFBibTeX XMLCite \textit{D. Venturi} et al., J. Fluid Mech. 606, 339--367 (2008; Zbl 1146.76018) Full Text: DOI
Foo, Jasmine; Yosibash, Zohar; Karniadakis, George Em Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties. (English) Zbl 1173.74464 Comput. Methods Appl. Mech. Eng. 196, No. 41-44, 4250-4271 (2007). MSC: 74S25 74E35 74S05 PDFBibTeX XMLCite \textit{J. Foo} et al., Comput. Methods Appl. Mech. Eng. 196, No. 41--44, 4250--4271 (2007; Zbl 1173.74464) Full Text: DOI
Wan, Xiaoliang; Karniadakis, George Em Long-term behavior of polynomial chaos in stochastic flow simulations. (English) Zbl 1123.76058 Comput. Methods Appl. Mech. Eng. 195, No. 41-43, 5582-5596 (2006). MSC: 76M35 PDFBibTeX XMLCite \textit{X. Wan} and \textit{G. E. Karniadakis}, Comput. Methods Appl. Mech. Eng. 195, No. 41--43, 5582--5596 (2006; Zbl 1123.76058) Full Text: DOI
Wan, X.; Karniadakis, G. E. Stochastic heat transfer enhancement in a grooved channel. (English) Zbl 1177.76091 J. Fluid Mech. 565, 255-278 (2006). MSC: 76D05 76M35 80A20 PDFBibTeX XMLCite \textit{X. Wan} and \textit{G. E. Karniadakis}, J. Fluid Mech. 565, 255--278 (2006; Zbl 1177.76091) Full Text: DOI
Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. Predicting shock dynamics in the presence of uncertainties. (English) Zbl 1146.76613 J. Comput. Phys. 217, No. 1, 260-276 (2006). MSC: 76L05 65P20 76J20 76M10 76M35 PDFBibTeX XMLCite \textit{G. Lin} et al., J. Comput. Phys. 217, No. 1, 260--276 (2006; Zbl 1146.76613) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Supersensitivity due to uncertain boundary conditions. (English) Zbl 1075.76623 Int. J. Numer. Methods Eng. 61, No. 12, 2114-2138 (2004). MSC: 76M22 76M10 76D06 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Int. J. Numer. Methods Eng. 61, No. 12, 2114--2138 (2004; Zbl 1075.76623) Full Text: DOI
Lin, Guang; Su, Chau-Hsing; Karniadakis, G. E. The stochastic piston problem. (English) Zbl 1135.76334 Proc. Natl. Acad. Sci. USA 101, No. 45, 15840-15845 (2004). MSC: 76M35 76L05 76N15 82C05 PDFBibTeX XMLCite \textit{G. Lin} et al., Proc. Natl. Acad. Sci. USA 101, No. 45, 15840--15845 (2004; Zbl 1135.76334) Full Text: DOI
Lucor, D.; Su, C.-H.; Karniadakis, G. E. Generalized polynomial chaos and random oscillators. (English) Zbl 1060.70515 Int. J. Numer. Methods Eng. 60, No. 3, 571-596 (2004). MSC: 70L05 70K55 70-08 PDFBibTeX XMLCite \textit{D. Lucor} et al., Int. J. Numer. Methods Eng. 60, No. 3, 571--596 (2004; Zbl 1060.70515) Full Text: DOI
Lucor, Didier; Karniadakis, George Em Predictability and uncertainty in flow–structure interactions. (English) Zbl 1045.76549 Eur. J. Mech., B, Fluids 23, No. 1, 41-49 (2004). MSC: 76M35 76-05 74F10 PDFBibTeX XMLCite \textit{D. Lucor} and \textit{G. E. Karniadakis}, Eur. J. Mech., B, Fluids 23, No. 1, 41--49 (2004; Zbl 1045.76549) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em A new stochastic approach to transient heat conduction modeling with uncertainty. (English) Zbl 1038.80003 Int. J. Heat Mass Transfer 46, No. 24, 4681-4693 (2003). MSC: 80A20 37N20 60H15 65C30 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, Int. J. Heat Mass Transfer 46, No. 24, 4681--4693 (2003; Zbl 1038.80003) Full Text: DOI
Lucor, D.; Xiu, D.; Su, C.-H.; Karniadakis, G. E. Predictability and uncertainty in CFD. (English) Zbl 1032.76662 Int. J. Numer. Methods Fluids 43, No. 5, 483-505 (2003). MSC: 76M35 76D05 PDFBibTeX XMLCite \textit{D. Lucor} et al., Int. J. Numer. Methods Fluids 43, No. 5, 483--505 (2003; Zbl 1032.76662) Full Text: DOI
Xiu, Dongbin; Karniadakis, George Em Modeling uncertainty in flow simulations via generalized polynomial chaos. (English) Zbl 1047.76111 J. Comput. Phys. 187, No. 1, 137-167 (2003). MSC: 76M35 76D05 PDFBibTeX XMLCite \textit{D. Xiu} and \textit{G. E. Karniadakis}, J. Comput. Phys. 187, No. 1, 137--167 (2003; Zbl 1047.76111) Full Text: DOI
Jardak, M.; Su, C.-H.; Karniadakis, G. E. Spectral polynomial chaos solutions of the stochastic advection equation. (English) Zbl 1001.76084 J. Sci. Comput. 17, No. 1-4, 319-338 (2002). MSC: 76M35 76M22 76R99 65C30 PDFBibTeX XMLCite \textit{M. Jardak} et al., J. Sci. Comput. 17, No. 1--4, 319--338 (2002; Zbl 1001.76084) Full Text: DOI