Edit Profile (opens in new tab) Karniadakis, George Em Co-Author Distance Author ID: karniadakis.george-em Published as: Karniadakis, George Em; Karniadakis, G. E.; Karniadakis, George E.; Karniadakis, George; Karniadakis, George Em.; Karniadakis, George E. M.; Em Karniadakis, George more...less Homepage: https://www.brown.edu/research/projects/crunch/george-karniadakis External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef Documents Indexed: 376 Publications since 1986, including 7 Books and 36 Additional arXiv Preprints 7 Contributions as Editor Co-Authors: 270 Co-Authors with 375 Joint Publications 7,590 Co-Co-Authors all top 5 Co-Authors 6 single-authored 20 Zhang, Zhongqiang 19 Mao, Zhiping 16 Venturi, Daniele 16 Wan, Xiaoliang 15 Perdikaris, Paris G. 15 Zayernouri, Mohsen 14 Li, Zhen 14 Sherwin, Spencer J. 14 Zeng, Fanhai 13 Meng, Xuhui 13 Raissi, Maziar 12 Jagtap, Ameya D. 12 Kirby, Robert M. II 12 Lu, Lu 12 Xiu, Dongbin 11 Triantafyllou, Michael S. 11 Wang, Zhi Cheng 10 Song, Fangying 9 Caswell, Bruce 9 Kawaguchi, Kenji 9 Lucor, Didier 9 Su, Chau-Hsing 9 Yu, Yue 8 Dong, Suchuan 8 Lin, Guang 8 Maxey, Martin R. 8 Pang, Guofei 7 Deng, Mingge 7 Evangelinos, Constantinos 7 Goswami, Somdatta 7 Grinberg, Leopold 7 Kharazmi, Ehsan 7 Lomtev, Igor 7 Orszag, Steven Alan 7 Rozovskii, Boris L. 7 Shin, Yeonjong 7 Yang, Liu 7 Zheng, Xiaoning 6 Babaee, Hessam 6 Cho, Heyrim 6 Choi, Minseok 6 Darbon, Jerome 6 Fedosov, Dmitry A. 6 Giannakouros, John G. 6 Guo, Ling 6 Hu, Zheyuan 6 Kahana, Adar 6 Shukla, Khemraj 6 Sirisup, Sirod 6 Zhang, Dongkun 6 Zou, Zongren 5 Bian, Xin 5 Constantinides, Yiannis 5 Henderson, Ronald D. 5 Ma, Xia 5 Sidilkover, David 5 Stinis, Panos 5 Warburton, Timothy 5 Yang, Xiu 5 Yin, Minglang 4 Ainsworth, Mark 4 Baek, Hyoungsu 4 Bittencourt, Marco Lúcio 4 Cai, Shengze 4 Cai, Wei 4 Cao, Wanrong 4 Gulian, Mamikon 4 Lei, Huan 4 Lischke, Anna 4 Patera, Anthony T. 4 Sapsis, Themistoklis P. 4 Symeonidis, Vasileios 4 Tang, Yuhang 4 Xu, Jin 4 Zaki, Tamer A. 4 Zhang, Zhen 3 Beskok, Ali 3 Chryssostomidis, Chryssostomos 3 Foo, Jasmine 3 Howard, Amanda A. 3 Kevrekidis, Ioannis George 3 Kim, Changho 3 Meng, Tingwei 3 Perego, Mauro 3 Peyvan, Ahmad 3 Psaros, Apostolos F. 3 Rockwell, Donald 3 Shu, Chi-Wang 3 Tang, Yifa 3 Tretyakov, Michael V. 3 Triantafyllou, George S. 3 Turkel, Eli L. 3 Yazdani, Alireza 3 Zhang, Enrui 3 Zheng, Mengdi 2 Batcho, Paul F. 2 Blumers, Ansel L. 2 Bora, Aniruddha 2 Bourguet, Rémi 2 Bravo, Luis G. ...and 170 more Co-Authors all top 5 Serials 105 Journal of Computational Physics 46 Computer Methods in Applied Mechanics and Engineering 40 SIAM Journal on Scientific Computing 31 Journal of Fluid Mechanics 9 Communications in Computational Physics 7 International Journal for Numerical Methods in Engineering 7 Journal of Scientific Computing 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 SIAM Journal on Numerical Analysis 4 Computational Mechanics 3 International Journal for Numerical Methods in Fluids 3 Applied Numerical Mathematics 3 Neural Networks 3 Fractional Calculus & Applied Analysis 3 Numerical Mathematics and Scientific Computation 2 Computers and Fluids 2 International Journal of Heat and Mass Transfer 2 Proceedings of the National Academy of Sciences of the United States of America 2 SIAM Review 2 European Journal of Mechanics. B. Fluids 2 Multiscale Modeling & Simulation 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Computers and Structures 1 Journal of Engineering Mathematics 1 Journal of Statistical Physics 1 Physics of Fluids, A 1 Fluid Dynamics Research 1 Theoretical and Computational Fluid Dynamics 1 Chaos, Solitons and Fractals 1 Bulletin of the Polish Academy of Sciences. Technical Sciences 1 Numerische Mathematik 1 Physica D 1 European Journal of Applied Mathematics 1 Journal of Non-Newtonian Fluid Mechanics 1 Physics of Fluids 1 Electronic Journal of Differential Equations (EJDE) 1 Parallel Algorithms and Applications 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Flow, Turbulence and Combustion 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 Applied Mathematical Sciences 1 Interdisciplinary Applied Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Science 1 Numerical Mathematics: Theory, Methods and Applications 1 International Journal for Uncertainty Quantification 1 Journal of Theoretical Biology 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Transactions of Mathematics and its Applications 1 Handbook of Fractional Calculus with Applications 1 Communications on Applied Mathematics and Computation all top 5 Fields 178 Fluid mechanics (76-XX) 163 Numerical analysis (65-XX) 87 Partial differential equations (35-XX) 56 Probability theory and stochastic processes (60-XX) 56 Computer science (68-XX) 40 Mechanics of deformable solids (74-XX) 26 Ordinary differential equations (34-XX) 25 Biology and other natural sciences (92-XX) 20 Statistics (62-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Geophysics (86-XX) 10 Real functions (26-XX) 10 Approximations and expansions (41-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 General and overarching topics; collections (00-XX) 7 Classical thermodynamics, heat transfer (80-XX) 4 Algebraic geometry (14-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 320 Publications have been cited 12,843 times in 6,832 Documents Cited by ▼ Year ▼ The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004 Xiu, Dongbin; Karniadakis, George Em 951 2002 Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Zbl 1415.68175 Raissi, M.; Perdikaris, P.; Karniadakis, G. E. 934 2019 High-order splitting methods for the incompressible Navier-Stokes equations. Zbl 0738.76050 Karniadakis, George Em; Israeli, Moshe; Orszag, Steven A. 427 1991 Spectral/\(hp\) element methods for computational fluid dynamics. 2nd ed. Zbl 1116.76002 Karniadakis, George Em; Sherwin, Spencer J. 390 2005 The development of discontinuous Galerkin methods. Zbl 0989.76045 Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang 354 2000 Modeling uncertainty in flow simulations via generalized polynomial chaos. Zbl 1047.76111 Xiu, Dongbin; Karniadakis, George Em 315 2003 Spectral/hp element methods for CFD. Zbl 0954.76001 Karniadakis, George Em; Sherwin, Spencer J. 285 1999 Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248 Raissi, Maziar; Karniadakis, George Em 216 2018 An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Zbl 1078.65008 Wan, Xiaoliang; Karniadakis, George Em 204 2005 Microflows and nanoflows. Fundamentals and simulation. Foreword by Chih-Ming Ho. Zbl 1115.76003 Karniadakis, George; Beskok, Ali; Narayan, Aluru 177 2005 DeepXDE: a deep learning library for solving differential equations. Zbl 1459.65002 Lu, Lu; Meng, Xuhui; Mao, Zhiping; Karniadakis, George Em 177 2021 Multi-element generalized polynomial chaos for arbitrary probability measures. Zbl 1128.65009 Wan, Xiaoliang; Karniadakis, George Em 170 2006 Fractional Sturm-Liouville eigen-problems: theory and numerical approximation. Zbl 1349.34095 Zayernouri, Mohsen; Karniadakis, George Em 161 2013 Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Zbl 1016.65001 Xiu, Dongbin; Karniadakis, George Em 156 2002 Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Zbl 1478.76057 Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em. 145 2020 Fractional spectral collocation method. Zbl 1294.65097 Zayernouri, Mohsen; Karniadakis, George Em 142 2014 What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179 Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em 139 2020 FPINNs: fractional physics-informed neural networks. Zbl 1420.35459 Pang, Guofei; Lu, Lu; Karniadakis, George Em 136 2019 Machine learning of linear differential equations using Gaussian processes. Zbl 1380.68339 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 135 2017 Spectral/\(hp\) element methods for computational fluid dynamics. Reprint of the 2nd hardback ed. (2005). Zbl 1256.76003 Karniadakis, George Em; Sherwin, Spencer J. 135 2013 Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Zbl 0746.76021 Deane, A. E.; Kevrekidis, I. G.; Karniadakis, G. E.; Orszag, S. A. 132 1991 Inferring solutions of differential equations using noisy multi-fidelity data. Zbl 1382.65229 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 121 2017 Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. Zbl 1349.65531 Zayernouri, Mohsen; Karniadakis, George Em 110 2015 Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems. Zbl 1442.92002 Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em 109 2020 Second-order approximations for variable order fractional derivatives: algorithms and applications. Zbl 1349.65092 Zhao, Xuan; Sun, Zhi-zhong; Karniadakis, George Em 106 2015 Physics-informed neural networks for high-speed flows. Zbl 1442.76092 Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em 106 2020 A semi-Lagrangian high-order method for Navier-Stokes equations. Zbl 1028.76026 Xiu, Dongbin; Karniadakis, George Em 102 2001 Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043 100 2000 A spectral vanishing viscosity method for large eddy simulations. Zbl 0984.76036 Karamanos, G. S.; Karniadakis, G. E. 99 2000 A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations. Zbl 1339.65197 Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 99 2015 Exponentially accurate spectral and spectral element methods for fractional ODEs. Zbl 1349.65257 Zayernouri, Mohsen; Karniadakis, George Em 98 2014 B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. Zbl 07508507 Yang, Liu; Meng, Xuhui; Karniadakis, George Em 93 2021 Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Zbl 07419158 Jagtap, Ameya D.; Karniadakis, George Em 90 2020 The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. Zbl 1153.65008 Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em 89 2008 A spectral viscosity method for correcting the long-term behavior of POD models. Zbl 1136.76412 Sirisup, S.; Karniadakis, G. E. 86 2004 Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Zbl 1453.68165 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 85 2020 Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. Zbl 1454.65008 Zhang, Dongkun; Lu, Lu; Guo, Ling; Karniadakis, George Em 84 2019 A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Zbl 1075.76621 Sherwin, S. J.; Karniadakis, G. E. 83 1995 Multi-element probabilistic collocation method in high dimensions. Zbl 1181.65014 Foo, Jasmine; Karniadakis, George Em 83 2010 Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. Zbl 1386.65030 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 77 2018 Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions. Zbl 1439.65081 Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 76 2017 A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127 Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em. 74 2015 A low-dimensional model for simulating three-dimensional cylinder flow. Zbl 1001.76043 Ma, Xia; Karniadakis, George Em 72 2002 Long-term behavior of polynomial chaos in stochastic flow simulations. Zbl 1123.76058 Wan, Xiaoliang; Karniadakis, George Em 70 2006 De-aliasing on non-uniform grids: algorithms and applications. Zbl 1161.76534 Kirby, Robert M.; Karniadakis, George Em 70 2003 Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. Zbl 0754.76043 Karniadakis, George Em; Triantafyllou, George S. 69 1992 hp-VPINNs: variational physics-informed neural networks with domain decomposition. Zbl 1506.68105 Kharazmi, Ehsan; Zhang, Zhongqiang; Karniadakis, George E. M. 67 2021 On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. Zbl 1473.65349 Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em 66 2020 A new triangular and tetrahedral basis for high-order \((hp)\) finite element methods. Zbl 0837.73075 Sherwin, Spencer J.; Karniadakis, George Em. 65 1995 Discontinuous spectral element methods for time- and space-fractional advection equations. Zbl 1304.35757 Zayernouri, Mohsen; Karniadakis, George Em 63 2014 NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations. Zbl 07510065 Jin, Xiaowei; Cai, Shengze; Li, Hui; Karniadakis, George Em 62 2021 A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems. Zbl 1454.76006 Meng, Xuhui; Karniadakis, George Em 59 2020 A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations. Zbl 1423.76102 Song, Fangying; Xu, Chuanju; Karniadakis, George Em 59 2016 Dynamics and low-dimensionality of a turbulent near wake. Zbl 0987.76041 Ma, X.; Karamanos, G.-S.; Karniadakis, G. E. 56 2000 Time-dependent generalized polynomial chaos. Zbl 1201.65216 Gerritsma, Marc; van der Steen, Jan-Bart; Vos, Peter; Karniadakis, George 56 2010 A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative. Zbl 1422.65428 Mao, Zhiping; Karniadakis, George Em 55 2018 Deep learning of vortex-induced vibrations. Zbl 1415.76177 Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em 55 2019 Reweighted \(\ell_1\) minimization method for stochastic elliptic differential equations. Zbl 1349.60113 Yang, Xiu; Karniadakis, George Em 54 2013 Numerical methods for stochastic partial differential equations with white noise. Zbl 1380.65021 Zhang, Zhongqiang; Karniadakis, George Em 54 2017 Physics-informed generative adversarial networks for stochastic differential equations. Zbl 1440.60065 Yang, Liu; Zhang, Dongkun; Karniadakis, George Em 53 2020 A discontinuous Galerkin ALE method for compressible viscous flows in moving domains. Zbl 0956.76046 Lomtev, I.; Kirby, R. M.; Karniadakis, G. E. 52 1999 Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks. Zbl 1440.60067 Zhang, Dongkun; Guo, Ling; Karniadakis, George Em 52 2020 Frequency selection and asymptotic states in laminar wakes. Zbl 0659.76043 Karniadakis, George Em; Triantafyllou, George S. 51 1989 Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. Zbl 1408.76428 Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em 51 2012 Micro flows. Fundamentals and simulation. Zbl 0998.76002 Karniadakis, George Em; Beskok, Ali 50 2002 A new stochastic approach to transient heat conduction modeling with uncertainty. Zbl 1038.80003 Xiu, Dongbin; Karniadakis, George Em 49 2003 Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions. Zbl 1355.65104 Cao, Wanrong; Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 49 2016 Beyond Wiener-Askey expansions: handling arbitrary PDFs. Zbl 1102.65006 Wan, Xiaoliang; Karniadakis, George Em 48 2006 Petrov-Galerkin and spectral collocation methods for distributed order differential equations. Zbl 1367.65113 Kharazmi, Ehsan; Zayernouri, Mohsen; Karniadakis, George Em 47 2017 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012 Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 47 2015 Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. Zbl 1352.65278 Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 46 2016 A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities. Zbl 1431.65193 Zeng, Fanhai; Mao, Zhiping; Karniadakis, George Em 46 2017 Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. Zbl 1407.62252 Perdikaris, P.; Raissi, M.; Damianou, A.; Lawrence, N. D.; Karniadakis, G. E. 46 2017 A discontinuous Galerkin method for the viscous MHD equations. Zbl 0954.76051 Warburton, T. C.; Karniadakis, G. E. 45 1999 Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step. Zbl 0728.76057 Kaiktsis, Lambros; Karniadakis, George Em; Orszag, Steven A. 45 1991 PPINN: parareal physics-informed neural network for time-dependent PDEs. Zbl 1506.65181 Meng, Xuhui; Li, Zhen; Zhang, Dongkun; Karniadakis, George Em 45 2020 A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. Zbl 1349.76569 Dong, S.; Karniadakis, G. E.; Chryssostomidis, C. 44 2014 A combined direct numerical simulation–particle image velocimetry study of the turbulent near wake. Zbl 1177.76156 Dong, S.; Karniadakis, G. E.; Ekmekci, A.; Rockwell, D. 43 2006 Tetrahedral spectral elements for CFD. Zbl 0857.76044 Sherwin, S. J.; Karniadakis, G. E. 42 1995 Spectral polynomial chaos solutions of the stochastic advection equation. Zbl 1001.76084 Jardak, M.; Su, C.-H.; Karniadakis, G. E. 42 2002 Spectral and discontinuous spectral element methods for fractional delay equations. Zbl 1314.34159 Zayernouri, Mohsen; Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em 39 2014 Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Zbl 1507.65217 Yu, Jeremy; Lu, Lu; Meng, Xuhui; Karniadakis, George Em 38 2022 nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. Zbl 07508384 Pang, G.; D’Elia, M.; Parks, M.; Karniadakis, G. E. 38 2020 Spectral element-Fourier methods for incompressible turbulent flows. Zbl 0722.76053 Karniadakis, G. E. 37 1990 Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations. Zbl 1326.65100 Zhang, Zhongqiang; Zeng, Fanhai; Karniadakis, George Em 37 2015 Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. Zbl 1415.74049 Yu, Yue; Perdikaris, Paris; Karniadakis, George Em 37 2016 Mechanisms of transverse motions in turbulent wall flows. Zbl 1039.76028 Karniadakis, G. E.; Choi, Kwing-So 36 2003 Systematic coarse-graining of spectrin-level red blood cell models. Zbl 1231.74311 Fedosov, Dmitry A.; Caswell, Bruce; Karniadakis, George Em 35 2010 Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Zbl 1472.68175 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 35 2020 A direct numerical simulation study of flow past a freely vibrating cable. Zbl 0901.76062 Newman, David J.; Karniadakis, George Em 34 1997 Unstructured spectral element methods for simulation of turbulent flows. Zbl 0840.76070 Henderson, Ronald D.; Karniadakis, George Em 33 1995 Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step. Zbl 0875.76111 Kaiktsis, Lambros; Karniadakis, George Em; Orszag, Steven A. 33 1996 Computing fractional Laplacians on complex-geometry domains: algorithms and simulations. Zbl 1380.65357 Song, Fangying; Xu, Chuanju; Karniadakis, George Em 33 2017 Adaptive finite element method for fractional differential equations using hierarchical matrices. Zbl 1439.65091 Zhao, Xuan; Hu, Xiaozhe; Cai, Wei; Karniadakis, George Em 33 2017 Spectral/hp methods for viscous compressible flows on unstructured 2D meshes. Zbl 0929.76095 Lomtev, I.; Quillen, C. B.; Karniadakis, G. E. 31 1998 Equation-free/Galerkin-free POD-assisted computation of incompressible flows. Zbl 1213.76146 Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G. 31 2005 Tetrahedral \(hp\) finite elements: Algorithms and flow simulations. Zbl 0847.76038 Sherwin, S. J.; Karniadakis, G. E. 30 1996 Generalized polynomial chaos and random oscillators. Zbl 1060.70515 Lucor, D.; Su, C.-H.; Karniadakis, G. E. 29 2004 Drag reduction in wall-bounded turbulence via a transverse travelling wave. Zbl 1112.76373 Du, Yiqing; Symeonidis, V.; Karniadakis, G. E. 29 2002 A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. Zbl 1426.76496 Baek, Hyoungsu; Karniadakis, George Em 28 2012 Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons. Zbl 07652802 Psaros, Apostolos F.; Meng, Xuhui; Zou, Zongren; Guo, Ling; Karniadakis, George Em 10 2023 Neural operator prediction of linear instability waves in high-speed boundary layers. Zbl 07640550 Clark Di Leoni, Patricio; Lu, Lu; Meneveau, Charles; Karniadakis, George Em; Zaki, Tamer A. 4 2023 On the influence of over-parameterization in manifold based surrogates and deep neural operators. Zbl 07660362 Kontolati, Katiana; Goswami, Somdatta; Shields, Michael D.; Karniadakis, George Em 4 2023 Reliable extrapolation of deep neural operators informed by physics or sparse observations. Zbl 07692973 Zhu, Min; Zhang, Handi; Jiao, Anran; Karniadakis, George Em; Lu, Lu 2 2023 A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions. Zbl 07748050 Penwarden, Michael; Jagtap, Ameya D.; Zhe, Shandian; Karniadakis, George Em; Kirby, Robert M. 1 2023 Accelerating gradient descent and Adam via fractional gradients. Zbl 07755615 Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em 1 2023 A hybrid deep neural operator/finite element method for ice-sheet modeling. Zbl 07742911 He, QiZhi; Perego, Mauro; Howard, Amanda A.; Karniadakis, George Em; Stinis, Panos 1 2023 Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Zbl 1507.65217 Yu, Jeremy; Lu, Lu; Meng, Xuhui; Karniadakis, George Em 38 2022 A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Zbl 1507.65050 Lu, Lu; Meng, Xuhui; Cai, Shengze; Mao, Zhiping; Goswami, Somdatta; Zhang, Zhongqiang; Karniadakis, George Em 23 2022 Error estimates for deeponets: a deep learning framework in infinite dimensions. Zbl 07525076 Lanthaler, Samuel; Mishra, Siddhartha; Karniadakis, George E. 22 2022 A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials. Zbl 1507.74383 Goswami, Somdatta; Yin, Minglang; Yu, Yue; Karniadakis, George Em 22 2022 Physics-informed neural networks for inverse problems in supersonic flows. Zbl 07561079 Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em 18 2022 Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems. Zbl 1507.74523 Yin, Minglang; Zhang, Enrui; Yu, Yue; Karniadakis, George Em 12 2022 Meta-learning PINN loss functions. Zbl 07527733 Psaros, Apostolos F.; Kawaguchi, Kenji; Karniadakis, George Em 11 2022 Bayesian physics informed neural networks for real-world nonlinear dynamical systems. Zbl 1507.68246 Linka, Kevin; Schäfer, Amelie; Meng, Xuhui; Zou, Zongren; Karniadakis, George Em; Kuhl, Ellen 10 2022 When do extended physics-informed neural networks (XPINNs) improve generalization? Zbl 1498.65183 Hu, Zheyuan; Jagtap, Ameya D.; Karniadakis, George Em; Kawaguchi, Kenji 10 2022 Learning functional priors and posteriors from data and physics. Zbl 1515.62046 Meng, Xuhui; Yang, Liu; Mao, Zhiping; del Águila Ferrandis, José; Karniadakis, George Em 9 2022 Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. Zbl 1503.65194 Zhang, Hui; Zeng, Fanhai; Jiang, Xiaoyun; Karniadakis, George Em 4 2022 SympOCnet: solving optimal control problems with applications to high-dimensional multiagent path planning problems. Zbl 1504.49052 Meng, Tingwei; Zhang, Zhen; Darbon, Jerome; Karniadakis, George 2 2022 Efficient and accurate numerical methods using the accelerated spectral deferred correction for solving fractional differential equations. Zbl 1524.65643 Chen, Xuejuan; Mao, Zhiping; Karniadakis, George Em 2 2022 Generative ensemble regression: Learning particle dynamics from observations of ensembles with physics-informed deep generative models. Zbl 1491.60117 Yang, Liu; Daskalakis, Constantinos; Karniadakis, George E. 2 2022 A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. Zbl 07525181 Zhao, Yue; Mao, Zhiping; Guo, Ling; Tang, Yifa; Karniadakis, George Em 1 2022 Fractional buffer layers: absorbing boundary conditions for wave propagation. Zbl 1485.35376 Cai, Min; Kharazmi, Ehsan; Li, Changpin; Karniadakis, George Em 1 2022 DeepXDE: a deep learning library for solving differential equations. Zbl 1459.65002 Lu, Lu; Meng, Xuhui; Mao, Zhiping; Karniadakis, George Em 177 2021 B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. Zbl 07508507 Yang, Liu; Meng, Xuhui; Karniadakis, George Em 93 2021 hp-VPINNs: variational physics-informed neural networks with domain decomposition. Zbl 1506.68105 Kharazmi, Ehsan; Zhang, Zhongqiang; Karniadakis, George E. M. 67 2021 NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations. Zbl 07510065 Jin, Xiaowei; Cai, Shengze; Li, Hui; Karniadakis, George Em 62 2021 DeepM&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks. Zbl 07513856 Cai, Shengze; Wang, Zhicheng; Lu, Lu; Zaki, Tamer A.; Karniadakis, George Em 24 2021 Parallel physics-informed neural networks via domain decomposition. Zbl 07516435 Shukla, Khemraj; Jagtap, Ameya D.; Karniadakis, George Em 23 2021 Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. Zbl 07516434 Lou, Qin; Meng, Xuhui; Karniadakis, George Em 21 2021 Towards a unified theory of fractional and nonlocal vector calculus. Zbl 1498.26008 D’Elia, Marta; Gulian, Mamikon; Olson, Hayley; Karniadakis, George Em 20 2021 Non-invasive inference of thrombus material properties with physics-informed neural networks. Zbl 1506.74215 Yin, Minglang; Zheng, Xiaoning; Humphrey, Jay D.; Karniadakis, George Em 19 2021 DeepM&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. Zbl 07516442 Mao, Zhiping; Lu, Lu; Marxen, Olaf; Zaki, Tamer A.; Karniadakis, George Em 18 2021 Multi-fidelity Bayesian neural networks: algorithms and applications. Zbl 07505956 Meng, Xuhui; Babaee, Hessam; Karniadakis, George Em 17 2021 Two-point stress-strain-rate correlation structure and non-local eddy viscosity in turbulent flows. Zbl 1461.76181 Clark Di Leoni, Patricio; Zaki, Tamer A.; Karniadakis, George; Meneveau, Charles 16 2021 Solving inverse stochastic problems from discrete particle observations using the Fokker-Planck equation and physics-informed neural networks. Zbl 1480.35377 Chen, Xiaoli; Yang, Liu; Duan, Jinqiao; Karniadakis, George Em 15 2021 Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks. Zbl 1461.76417 Cai, Shengze; Wang, Zhicheng; Fuest, Frederik; Jeon, Young Jin; Gray, Callum; Karniadakis, George Em 14 2021 Learning and meta-learning of stochastic advection-diffusion-reaction systems from sparse measurements. Zbl 07441294 Chen, Xiaoli; Duan, Jinqiao; Karniadakis, George Em 13 2021 A seamless multiscale operator neural network for inferring bubble dynamics. Zbl 1495.76119 Lin, Chensen; Maxey, Martin; Li, Zhen; Karniadakis, George Em 11 2021 A fast multi-fidelity method with uncertainty quantification for complex data correlations: application to vortex-induced vibrations of marine risers. Zbl 1507.62298 Meng, Xuhui; Wang, Zhicheng; Fan, Dixia; Triantafyllou, Michael S.; Karniadakis, George Em 3 2021 A phase-field method for boiling heat transfer. Zbl 07503725 Wang, Zhicheng; Zheng, Xiaoning; Chryssostomidis, Chryssostomos; Karniadakis, George Em 3 2021 Multiscale parareal algorithm for long-time mesoscopic simulations of microvascular blood flow in zebrafish. Zbl 1479.76123 Blumers, Ansel L.; Yin, Minglang; Nakajima, Hiroyuki; Hasegawa, Yosuke; Li, Zhen; Karniadakis, George Em 2 2021 Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows. Zbl 07510254 Zhao, Lifei; Li, Zhen; Wang, Zhicheng; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em 2 2021 An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains. Zbl 07690829 Carlson, Max; Zheng, Xiaoning; Sundar, Hari; Karniadakis, George Em; Kirby, Robert M. 1 2021 Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Zbl 1478.76057 Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em. 145 2020 What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179 Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em 139 2020 Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems. Zbl 1442.92002 Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em 109 2020 Physics-informed neural networks for high-speed flows. Zbl 1442.76092 Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em 106 2020 Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Zbl 07419158 Jagtap, Ameya D.; Karniadakis, George Em 90 2020 Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Zbl 1453.68165 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 85 2020 On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. Zbl 1473.65349 Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em 66 2020 A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems. Zbl 1454.76006 Meng, Xuhui; Karniadakis, George Em 59 2020 Physics-informed generative adversarial networks for stochastic differential equations. Zbl 1440.60065 Yang, Liu; Zhang, Dongkun; Karniadakis, George Em 53 2020 Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks. Zbl 1440.60067 Zhang, Dongkun; Guo, Ling; Karniadakis, George Em 52 2020 PPINN: parareal physics-informed neural network for time-dependent PDEs. Zbl 1506.65181 Meng, Xuhui; Li, Zhen; Zhang, Dongkun; Karniadakis, George Em 45 2020 nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. Zbl 07508384 Pang, G.; D’Elia, M.; Parks, M.; Karniadakis, G. E. 38 2020 Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Zbl 1472.68175 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 35 2020 Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Zbl 1475.68316 Jin, Pengzhan; Zhang, Zhen; Zhu, Aiqing; Tang, Yifa; Karniadakis, George Em 27 2020 A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations. Zbl 1453.65370 Zhang, Hui; Jiang, Xiaoyun; Zeng, Fanhai; Karniadakis, George Em 20 2020 Dying ReLU and initialization: theory and numerical examples. Zbl 1507.68248 Lu, Lu; Shin, Yeonjong; Su, Yanhui; Karniadakis, George Em 11 2020 A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation. Zbl 1442.65144 Li, Xianjuan; Mao, Zhiping; Wang, Nan; Song, Fangying; Wang, Hong; Karniadakis, George Em 8 2020 Physics-informed semantic inpainting: application to geostatistical modeling. Zbl 07507237 Zheng, Qiang; Zeng, Lingzao; Karniadakis, George Em 7 2020 Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. Zbl 1475.68315 Jin, Pengzhan; Lu, Lu; Tang, Yifa; Karniadakis, George Em 5 2020 Fractional calculus and numerical methods for fractional PDEs. Zbl 1442.35514 Kharazmi, Ehsan; Mao, Zhiping; Pang, Guofei; Zayernouri, Mohsen; Karniadakis, George Em 1 2020 Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Zbl 1415.68175 Raissi, M.; Perdikaris, P.; Karniadakis, G. E. 934 2019 FPINNs: fractional physics-informed neural networks. Zbl 1420.35459 Pang, Guofei; Lu, Lu; Karniadakis, George Em 136 2019 Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. Zbl 1454.65008 Zhang, Dongkun; Lu, Lu; Guo, Ling; Karniadakis, George Em 84 2019 Deep learning of vortex-induced vibrations. Zbl 1415.76177 Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em 55 2019 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350 Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 26 2019 Machine learning of space-fractional differential equations. Zbl 1419.35209 Gulian, Mamikon; Raissi, Maziar; Perdikaris, Paris; Karniadakis, George 17 2019 Neural-net-induced Gaussian process regression for function approximation and PDE solution. Zbl 1451.68242 Pang, Guofei; Yang, Liu; Karniadakis, George Em 16 2019 Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations. Zbl 1440.65258 Zhao, Tinggang; Mao, Zhiping; Karniadakis, George Em 15 2019 Fractional Gray-Scott model: well-posedness, discretization, and simulations. Zbl 1440.35344 Wang, Tingting; Song, Fangying; Wang, Hong; Karniadakis, George Em 14 2019 Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network. Zbl 1434.76053 Mehta, Pavan Pranjivan; Pang, Guofei; Song, Fangying; Karniadakis, George Em 11 2019 Nonlocal flocking dynamics: learning the fractional order of PDEs from particle simulations. Zbl 1449.35447 Mao, Zhiping; Li, Zhen; Karniadakis, George Em 8 2019 An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe. Zbl 1415.76369 Wang, Zhicheng; Triantafyllou, Michael S.; Constantinides, Yiannis; Karniadakis, George Em 6 2019 Fractional magneto-hydrodynamics: algorithms and applications. Zbl 1416.76127 Song, Fangying; Karniadakis, George Em 5 2019 Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: application to hydrodynamics. Zbl 1452.76172 Blumers, Ansel L.; Li, Zhen; Karniadakis, George Em 4 2019 A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio. Zbl 1453.76154 Wang, Zhicheng; Dong, Suchuan; Triantafyllou, Michael S.; Constantinides, Yiannis; Karniadakis, George Em 4 2019 Numerical methods. Zbl 1410.65001 4 2019 One-dimensional modeling of fractional flow reserve in coronary artery disease: uncertainty quantification and Bayesian optimization. Zbl 1441.76150 Yin, Minglang; Yazdani, Alireza; Karniadakis, George Em 3 2019 A Computational Mechanics special issue on: Data-driven modeling and simulation – theory, methods, and applications. Zbl 1476.00073 3 2019 A spectral penalty method for two-sided fractional differential equations with general boundary conditions. Zbl 1501.65143 Wang, Nan; Mao, Zhiping; Huang, Chengming; Karniadakis, George Em 3 2019 Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow. Zbl 1430.76091 Fan, Dixia; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em 2 2019 Parametric Gaussian process regression for big data. Zbl 1471.62272 Raissi, Maziar; Babaee, Hessam; Karniadakis, George Em 1 2019 Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248 Raissi, Maziar; Karniadakis, George Em 216 2018 Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. Zbl 1386.65030 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 77 2018 A spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative. Zbl 1422.65428 Mao, Zhiping; Karniadakis, George Em 55 2018 A partitioned coupling framework for peridynamics and classical theory: analysis and simulations. Zbl 1440.74045 Yu, Yue; Bargos, Fabiano F.; You, Huaiqian; Parks, Michael L.; Bittencourt, Marco L.; Karniadakis, George E. 21 2018 A Riesz basis Galerkin method for the tempered fractional Laplacian. Zbl 1402.65120 Zhang, Zhijiang; Deng, Weihua; Karniadakis, George Em 21 2018 A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. Zbl 1404.65105 Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 18 2018 A dissipative particle dynamics method for arbitrarily complex geometries. Zbl 1380.76123 Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em 10 2018 A computational stochastic methodology for the design of random meta-materials under geometric constraints. Zbl 1398.60073 Tsantili, Ivi C.; Cho, Min Hyung; Cai, Wei; Karniadakis, George Em 10 2018 Multi-fidelity optimization of super-cavitating hydrofoils. Zbl 1439.74256 Bonfiglio, L.; Perdikaris, P.; Brizzolara, S.; Karniadakis, G. E. 10 2018 Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. Zbl 1392.76058 Zhao, Lifei; Li, Zhen; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em 6 2018 Stochastic domain decomposition via moment minimization. Zbl 1391.60167 Zhang, Dongkun; Babaee, Hessam; Karniadakis, George Em 4 2018 A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems. Zbl 1410.76320 Wang, Zhicheng; Triantafyllou, Michael S.; Constantinides, Yiannis; Karniadakis, George Em 3 2018 Analytical and computational studies of correlations of hydrodynamic fluctuations in shear flow. Zbl 1488.76101 Bian, Xin; Deng, Mingge; Karniadakis, George Em 2 2018 Machine learning of linear differential equations using Gaussian processes. Zbl 1380.68339 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 135 2017 Inferring solutions of differential equations using noisy multi-fidelity data. Zbl 1382.65229 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 121 2017 ...and 220 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 10,077 Authors 229 Karniadakis, George Em 74 Sherwin, Spencer J. 63 Wang, Hong 57 Lin, Guang 52 Kirby, Robert M. II 49 Zheng, Xiangcheng 42 Xiu, Dongbin 37 Dong, Suchuan 34 Doostan, Alireza 33 Rozza, Gianluigi 32 Narayan, Akil C. 32 Thompson, Mark Christopher 31 Schwab, Christoph 30 Liu, Fawang 29 Shen, Jie 28 Dehghan Takht Fooladi, Mehdi 28 Venturi, Daniele 27 Perdikaris, Paris G. 26 Ghanem, Roger G. 26 Hesthaven, Jan S. 26 Li, Hong 26 Liu, Yang 26 Zaky, Mahmoud A. 24 D’Elia, Marta 24 Dumbser, Michael 24 Kopriva, David Alan 24 Shu, Chi-Wang 24 Zhou, Tao 23 Mao, Zhiping 23 Zhang, Zhimin 22 Hourigan, Kerry 22 Zabaras, Nicholas J. 22 Zayernouri, Mohsen 22 Zeng, Fanhai 21 Blackburn, Hugh M. 21 Gassner, Gregor J. 21 Jiang, Xiaoyun 21 Tartakovsky, Daniel M. 21 Yu, Yue 21 Zhang, Zhongqiang 20 Baccouch, Mahboub 20 Ferrer, Esteban 20 Le Maître, Olivier P. 20 Mishra, Siddhartha 20 Nobile, Fabio 20 Wan, Xiaoliang 20 Wang, Lilian 20 Xu, Chuanju 20 Zhang, Dongxiao 19 Jin, Shi 19 Knio, Omar M. 19 Li, Zhen 19 Lucor, Didier 19 Tartakovsky, Alexandre M. 19 Turner, Ian William 19 Warburton, Timothy 19 Yang, Xiu 18 Abbaszadeh, Mostafa 18 Brunton, Steven L. 18 Guo, Ling 18 Iaccarino, Gianluca 18 Jakeman, John Davis 18 Kevrekidis, Ioannis George 18 Quarteroni, Alfio M. 18 Sagaut, Pierre 18 Xing, Yulong 17 Giraldo, Francis X. 17 Gunzburger, Max D. 17 Nordström, Jan 17 Pasquetti, Richard 16 Ainsworth, Mark 16 Cao, Wanrong 16 Cheng, Liang 16 Deng, Weihua 16 Guo, Ben-Yu 16 Kutz, J. Nathan 16 Machado, José António Tenreiro 16 Najm, Habib N. 16 Noack, Bernd R. 16 Peiró, Joaquim 16 Soize, Christian 16 Trask, Nathaniel A. 15 Elman, Howard C. 15 Hao, Zhaopeng 15 Heydari, Mohammad Hossein 15 Jornet, Marc 15 Kronbichler, Martin 15 Li, Dongfang 15 Matthies, Hermann Georg 15 Rubio, Gonzalo 15 Sheard, Gregory John 15 Zhang, Zhiwen 14 Boscheri, Walter 14 Lu, Lu 14 Luo, Hong 14 Manzoni, Andrea 14 Meng, Xuhui 14 Moxey, David 14 Pulch, Roland 14 Seaïd, Mohammed ...and 9,977 more Authors all top 5 Cited in 402 Serials 1,275 Journal of Computational Physics 631 Computer Methods in Applied Mechanics and Engineering 358 Journal of Scientific Computing 320 Journal of Fluid Mechanics 313 Computers and Fluids 209 SIAM Journal on Scientific Computing 183 Computers & Mathematics with Applications 138 Journal of Computational and Applied Mathematics 132 Applied Numerical Mathematics 127 Physics of Fluids 106 Applied Mathematics and Computation 100 International Journal for Numerical Methods in Engineering 89 Applied Mathematical Modelling 82 SIAM/ASA Journal on Uncertainty Quantification 74 Computational Mechanics 72 Communications in Computational Physics 67 Mathematics and Computers in Simulation 65 International Journal for Numerical Methods in Fluids 61 Physica D 60 Communications in Nonlinear Science and Numerical Simulation 56 Numerical Algorithms 54 Mathematics of Computation 54 International Journal of Computer Mathematics 51 European Journal of Mechanics. 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Electronic Transactions on Numerical Analysis 7 Vietnam Journal of Mathematics ...and 302 more Serials all top 5 Cited in 50 Fields 4,097 Numerical analysis (65-XX) 2,667 Fluid mechanics (76-XX) 2,108 Partial differential equations (35-XX) 825 Computer science (68-XX) 705 Mechanics of deformable solids (74-XX) 627 Probability theory and stochastic processes (60-XX) 373 Statistics (62-XX) 351 Real functions (26-XX) 331 Biology and other natural sciences (92-XX) 327 Ordinary differential equations (34-XX) 197 Statistical mechanics, structure of matter (82-XX) 191 Dynamical systems and ergodic theory (37-XX) 179 Approximations and expansions (41-XX) 154 Systems theory; control (93-XX) 147 Classical thermodynamics, heat transfer (80-XX) 136 Calculus of variations and optimal control; optimization (49-XX) 136 Geophysics (86-XX) 130 Optics, electromagnetic theory (78-XX) 101 Operations research, mathematical programming (90-XX) 84 Special functions (33-XX) 75 Integral equations (45-XX) 66 Mechanics of particles and systems (70-XX) 52 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Harmonic analysis on Euclidean spaces (42-XX) 47 Operator theory (47-XX) 47 Information and communication theory, circuits (94-XX) 46 Linear and multilinear algebra; matrix theory (15-XX) 39 Quantum theory (81-XX) 28 Functional analysis (46-XX) 19 Global analysis, analysis on manifolds (58-XX) 16 Difference and functional equations (39-XX) 15 General and overarching topics; collections (00-XX) 15 Integral transforms, operational calculus (44-XX) 10 Astronomy and astrophysics (85-XX) 9 Functions of a complex variable (30-XX) 8 Differential geometry (53-XX) 6 Potential theory (31-XX) 5 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Measure and integration (28-XX) 5 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 General topology (54-XX) 2 Mathematics education (97-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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