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: 371 Publications since 1986, including 8 Books and 14 Additional arXiv Preprints 7 Contributions as Editor Software Indexed: 15 Packages Co-Authors: 276 Co-Authors with 370 Joint Publications 7,672 Co-Co-Authors all top 5 Co-Authors 6 single-authored 21 Zhang, Zhongqiang 18 Mao, Zhiping 16 Venturi, Daniele 16 Wan, Xiaoliang 16 Zayernouri, Mohsen 14 Li, Zhen 14 Meng, Xuhui 14 Perdikaris, Paris G. 14 Sherwin, Spencer J. 14 Zeng, Fanhai 12 Lu, Lu 12 Xiu, Dongbin 11 Jagtap, Ameya D. 11 Kirby, Robert M. II 11 Raissi, Maziar 11 Triantafyllou, Michael S. 11 Wang, Zhi Cheng 10 Song, Fangying 9 Caswell, Bruce 9 Lucor, Didier 9 Su, Chau-Hsing 8 Dong, Suchuan 8 Lin, Guang 8 Maxey, Martin R. 8 Pang, Guofei 8 Yu, Yue 8 Zou, Zongren 7 Darbon, Jerome 7 Deng, Mingge 7 Evangelinos, Constantinos 7 Grinberg, Leopold 7 Kawaguchi, Kenji 7 Lomtev, Igor 7 Orszag, Steven Alan 7 Rozovskii, Boris L. 7 Yang, Liu 7 Zheng, Xiaoning 6 Babaee, Hessam 6 Cho, Heyrim 6 Choi, Minseok 6 Fedosov, Dmitry A. 6 Giannakouros, John G. 6 Guo, Ling 6 Kharazmi, Ehsan 6 Shin, Yeonjong 6 Sirisup, Sirod 6 Zhang, Dongkun 5 Bian, Xin 5 Constantinides, Yiannis 5 Goswami, Somdatta 5 Henderson, Ronald D. 5 Ma, Xia 5 Sidilkover, David 5 Warburton, Timothy 5 Yin, Minglang 5 Zhang, Zhen 4 Ainsworth, Mark 4 Baek, Hyoungsu 4 Bittencourt, Marco Lúcio 4 Cai, Shengze 4 Cai, Wei 4 Cao, Wanrong 4 Gulian, Mamikon 4 Hu, Zheyuan 4 Kahana, Adar 4 Lei, Huan 4 Lischke, Anna 4 Patera, Anthony T. 4 Sapsis, Themistoklis P. 4 Shukla, Khemraj 4 Symeonidis, Vasileios 4 Tang, Yuhang 4 Xu, Jin 4 Yang, Xiu 4 Zaki, Tamer A. 3 Beskok, Ali 3 Chryssostomidis, Chryssostomos 3 Foo, Jasmine 3 Kevrekidis, Ioannis George 3 Kim, Changho 3 Kopaničáková, Alena 3 Meng, Tingwei 3 Psaros, Apostolos F. 3 Rockwell, Donald 3 Shu, Chi-Wang 3 Stinis, Panos 3 Tang, Yifa 3 Tretyakov, Michael V. 3 Triantafyllou, George S. 3 Yazdani, Alireza 3 Zhang, Enrui 3 Zheng, Mengdi 2 Batcho, Paul F. 2 Blumers, Ansel L. 2 Bonfiglio, Luca 2 Bourguet, Rémi 2 Burrage, Kevin 2 Chen, Paula 2 Chen, Xiaoli 2 Chen, Xuejuan ...and 176 more Co-Authors all top 5 Serials 108 Journal of Computational Physics 53 Computer Methods in Applied Mechanics and Engineering 42 SIAM Journal on Scientific Computing 31 Journal of Fluid Mechanics 10 Communications in Computational Physics 8 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 4 Neural Networks 3 International Journal for Numerical Methods in Fluids 3 Applied Numerical Mathematics 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 Cambridge Monographs on Applied and Computational 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 SIAM/ASA Journal on Uncertainty Quantification 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 181 Fluid mechanics (76-XX) 175 Numerical analysis (65-XX) 93 Partial differential equations (35-XX) 68 Computer science (68-XX) 56 Probability theory and stochastic processes (60-XX) 41 Mechanics of deformable solids (74-XX) 28 Ordinary differential equations (34-XX) 25 Biology and other natural sciences (92-XX) 22 Statistics (62-XX) 11 Approximations and expansions (41-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Geophysics (86-XX) 9 Real functions (26-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 General and overarching topics; collections (00-XX) 6 Classical thermodynamics, heat transfer (80-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 335 Publications have been cited 15,488 times in 8,093 Documents Cited by ▼ Year ▼ 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. 1,362 2019 The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004 Xiu, Dongbin; Karniadakis, George Em 1,049 2002 Spectral/\(hp\) element methods for computational fluid dynamics. 2nd ed. Zbl 1116.76002 Karniadakis, George Em; Sherwin, Spencer J. 493 2005 High-order splitting methods for the incompressible Navier-Stokes equations. Zbl 0738.76050 Karniadakis, George Em; Israeli, Moshe; Orszag, Steven A. 450 1991 The development of discontinuous Galerkin methods. Zbl 0989.76045 Cockburn, Bernardo; Karniadakis, George E.; Shu, Chi-Wang 401 2000 Modeling uncertainty in flow simulations via generalized polynomial chaos. Zbl 1047.76111 Xiu, Dongbin; Karniadakis, George Em 336 2003 Spectral/hp element methods for CFD. Zbl 0954.76001 Karniadakis, George Em; Sherwin, Spencer J. 313 1999 DeepXDE: a deep learning library for solving differential equations. Zbl 1459.65002 Lu, Lu; Meng, Xuhui; Mao, Zhiping; Karniadakis, George Em 276 2021 Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248 Raissi, Maziar; Karniadakis, George Em 256 2018 An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Zbl 1078.65008 Wan, Xiaoliang; Karniadakis, George Em 215 2005 Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Zbl 1478.76057 Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em. 200 2020 Microflows and nanoflows. Fundamentals and simulation. Foreword by Chih-Ming Ho. Zbl 1115.76003 Karniadakis, George; Beskok, Ali; Narayan, Aluru 195 2005 FPINNs: fractional physics-informed neural networks. Zbl 1420.35459 Pang, Guofei; Lu, Lu; Karniadakis, George Em 195 2019 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 192 2020 Multi-element generalized polynomial chaos for arbitrary probability measures. Zbl 1128.65009 Wan, Xiaoliang; Karniadakis, George Em 179 2006 Fractional Sturm-Liouville eigen-problems: theory and numerical approximation. Zbl 1349.34095 Zayernouri, Mohsen; Karniadakis, George Em 176 2013 Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Zbl 1016.65001 Xiu, Dongbin; Karniadakis, George Em 169 2002 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 168 2020 Fractional spectral collocation method. Zbl 1294.65097 Zayernouri, Mohsen; Karniadakis, George Em 167 2014 Machine learning of linear differential equations using Gaussian processes. Zbl 1380.68339 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 159 2017 Physics-informed neural networks for high-speed flows. Zbl 1442.76092 Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em 152 2020 Spectral/\(hp\) element methods for computational fluid dynamics. Reprint of the 2nd hardback ed. (2005). Zbl 1256.76003 Karniadakis, George Em; Sherwin, Spencer J. 146 2013 Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Zbl 1542.65182 Jagtap, Ameya D.; Karniadakis, George Em 145 2020 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 141 2021 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. 139 1991 Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Zbl 1453.68165 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 135 2020 Inferring solutions of differential equations using noisy multi-fidelity data. Zbl 1382.65229 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 132 2017 Second-order approximations for variable order fractional derivatives: algorithms and applications. Zbl 1349.65092 Zhao, Xuan; Sun, Zhi-zhong; Karniadakis, George Em 126 2015 Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24–26, 1999. Zbl 0935.00043 123 2000 Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. Zbl 1349.65531 Zayernouri, Mohsen; Karniadakis, George Em 118 2015 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 111 2019 A semi-Lagrangian high-order method for Navier-Stokes equations. Zbl 1028.76026 Xiu, Dongbin; Karniadakis, George Em 109 2001 A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations. Zbl 1339.65197 Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 108 2015 A spectral vanishing viscosity method for large eddy simulations. Zbl 0984.76036 Karamanos, G. S.; Karniadakis, G. E. 107 2000 Exponentially accurate spectral and spectral element methods for fractional ODEs. Zbl 1349.65257 Zayernouri, Mohsen; Karniadakis, George Em 106 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 105 2021 hp-VPINNs: variational physics-informed neural networks with domain decomposition. Zbl 1506.68105 Kharazmi, Ehsan; Zhang, Zhongqiang; Karniadakis, George E. M. 103 2021 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 97 2017 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 93 2020 Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. Zbl 1386.65030 Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em 92 2018 The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. Zbl 1153.65008 Foo, Jasmine; Wan, Xiaoliang; Karniadakis, George Em 90 2008 A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Zbl 1075.76621 Sherwin, S. J.; Karniadakis, G. E. 89 1995 A spectral viscosity method for correcting the long-term behavior of POD models. Zbl 1136.76412 Sirisup, S.; Karniadakis, G. E. 88 2004 Multi-element probabilistic collocation method in high dimensions. Zbl 1181.65014 Foo, Jasmine; Karniadakis, George Em 86 2010 A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127 Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em. 83 2015 Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Zbl 1507.65217 Yu, Jeremy; Lu, Lu; Meng, Xuhui; Karniadakis, George Em 79 2022 De-aliasing on non-uniform grids: algorithms and applications. Zbl 1161.76534 Kirby, Robert M.; Karniadakis, George Em 75 2003 Physics-informed generative adversarial networks for stochastic differential equations. Zbl 1440.60065 Yang, Liu; Zhang, Dongkun; Karniadakis, George Em 74 2020 Discontinuous spectral element methods for time- and space-fractional advection equations. Zbl 1304.35757 Zayernouri, Mohsen; Karniadakis, George Em 73 2014 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 72 2006 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 72 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 72 2016 Micro flows. Fundamentals and simulation. Zbl 0998.76002 Karniadakis, George Em; Beskok, Ali 71 2002 Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. Zbl 0754.76043 Karniadakis, George Em; Triantafyllou, George S. 71 1992 A new triangular and tetrahedral basis for high-order \((hp)\) finite element methods. Zbl 0837.73075 Sherwin, Spencer J.; Karniadakis, George Em. 70 1995 Learning in modal space: solving time-dependent stochastic PDEs using physics-informed neural networks. Zbl 1440.60067 Zhang, Dongkun; Guo, Ling; Karniadakis, George Em 70 2020 Numerical methods for stochastic partial differential equations with white noise. Zbl 1380.65021 Zhang, Zhongqiang; Karniadakis, George Em 67 2017 PPINN: parareal physics-informed neural network for time-dependent PDEs. Zbl 1506.65181 Meng, Xuhui; Li, Zhen; Zhang, Dongkun; Karniadakis, George Em 66 2020 Time-dependent generalized polynomial chaos. Zbl 1201.65216 Gerritsma, Marc; van der Steen, Jan-Bart; Vos, Peter; Karniadakis, George 63 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 63 2018 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 63 2022 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. 60 2017 Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions. Zbl 1355.65104 Cao, Wanrong; Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 60 2016 Dynamics and low-dimensionality of a turbulent near wake. Zbl 0987.76041 Ma, X.; Karamanos, G.-S.; Karniadakis, G. E. 59 2000 Deep learning of vortex-induced vibrations. Zbl 1415.76177 Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em 59 2019 A discontinuous Galerkin ALE method for compressible viscous flows in moving domains. Zbl 0956.76046 Lomtev, I.; Kirby, R. M.; Karniadakis, G. E. 57 1999 Reweighted \(\ell_1\) minimization method for stochastic elliptic differential equations. Zbl 1349.60113 Yang, Xiu; Karniadakis, George Em 57 2013 Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. Zbl 1352.65278 Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em 55 2016 A new stochastic approach to transient heat conduction modeling with uncertainty. Zbl 1038.80003 Xiu, Dongbin; Karniadakis, George Em 53 2003 Parallel physics-informed neural networks via domain decomposition. Zbl 07516435 Shukla, Khemraj; Jagtap, Ameya D.; Karniadakis, George Em 53 2021 Frequency selection and asymptotic states in laminar wakes. Zbl 0659.76043 Karniadakis, George Em; Triantafyllou, George S. 52 1989 Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. Zbl 1408.76428 Yang, Xiu; Choi, Minseok; Lin, Guang; Karniadakis, George Em 52 2012 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012 Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 52 2015 A discontinuous Galerkin method for the viscous MHD equations. Zbl 0954.76051 Warburton, T. C.; Karniadakis, G. E. 51 1999 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 51 2017 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 51 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. 51 2014 Beyond Wiener-Askey expansions: handling arbitrary PDFs. Zbl 1102.65006 Wan, Xiaoliang; Karniadakis, George Em 50 2006 Petrov-Galerkin and spectral collocation methods for distributed order differential equations. Zbl 1367.65113 Kharazmi, Ehsan; Zayernouri, Mohsen; Karniadakis, George Em 50 2017 Error estimates for deeponets: a deep learning framework in infinite dimensions. Zbl 07525076 Lanthaler, Samuel; Mishra, Siddhartha; Karniadakis, George E. 49 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. 48 2020 Spectral and discontinuous spectral element methods for fractional delay equations. Zbl 1314.34159 Zayernouri, Mohsen; Cao, Wanrong; Zhang, Zhongqiang; Karniadakis, George Em 46 2014 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. 46 1991 Adaptive finite element method for fractional differential equations using hierarchical matrices. Zbl 1439.65091 Zhao, Xuan; Hu, Xiaozhe; Cai, Wei; Karniadakis, George Em 46 2017 Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. Zbl 1415.74049 Yu, Yue; Perdikaris, Paris; Karniadakis, George Em 45 2016 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. 44 2006 Spectral polynomial chaos solutions of the stochastic advection equation. Zbl 1001.76084 Jardak, M.; Su, C.-H.; Karniadakis, G. E. 43 2002 Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Zbl 1475.68316 Jin, Pengzhan; Zhang, Zhen; Zhu, Aiqing; Tang, Yifa; Karniadakis, George Em 43 2020 Tetrahedral spectral elements for CFD. Zbl 0857.76044 Sherwin, S. J.; Karniadakis, G. E. 42 1995 Spectral element-Fourier methods for incompressible turbulent flows. Zbl 0722.76053 Karniadakis, G. E. 39 1990 Systematic coarse-graining of spectrin-level red blood cell models. Zbl 1231.74311 Fedosov, Dmitry A.; Caswell, Bruce; Karniadakis, George Em 39 2010 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 39 2022 Computing fractional Laplacians on complex-geometry domains: algorithms and simulations. Zbl 1380.65357 Song, Fangying; Xu, Chuanju; Karniadakis, George Em 38 2017 Mechanisms of transverse motions in turbulent wall flows. Zbl 1039.76028 Karniadakis, G. E.; Choi, Kwing-So 37 2003 A direct numerical simulation study of flow past a freely vibrating cable. Zbl 0901.76062 Newman, David J.; Karniadakis, George Em 37 1997 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 Equation-free/Galerkin-free POD-assisted computation of incompressible flows. Zbl 1213.76146 Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin; Kevrekidis, Ioannis G. 35 2005 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 35 2021 Unstructured spectral element methods for simulation of turbulent flows. Zbl 0840.76070 Henderson, Ronald D.; Karniadakis, George Em 34 1995 Discovering a reaction-diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression. Zbl 1539.92006 Zhang, Zhen; Zou, Zongren; Kuhl, Ellen; Karniadakis, George Em 5 2024 NeuralUQ: a comprehensive library for uncertainty quantification in neural differential equations and operators. Zbl 1535.65005 Zou, Zongren; Meng, Xuhui; Psaros, Apostolos F.; Karniadakis, George E. 5 2024 Residual-based attention in physics-informed neural networks. Zbl 1539.65132 Anagnostopoulos, Sokratis J.; Toscano, Juan Diego; Stergiopulos, Nikolaos; Karniadakis, George Em 4 2024 Correcting model misspecification in physics-informed neural networks (PINNs). Zbl 07842894 Zou, Zongren; Meng, Xuhui; Karniadakis, George Em 3 2024 Learning stiff chemical kinetics using extended deep neural operators. Zbl 1539.92010 Goswami, Somdatta; Jagtap, Ameya D.; Babaee, Hessam; Susi, Bryan T.; Karniadakis, George Em 2 2024 Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. Zbl 07842893 Song, Jin; Zhong, Ming; Karniadakis, George Em; Yan, Zhenya 2 2024 Leveraging multitime Hamilton-Jacobi PDEs for certain scientific machine learning problems. Zbl 1537.35157 Chen, Paula; Meng, Tingwei; Zou, Zongren; Darbon, Jérôme; Karniadakis, George Em 2 2024 Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks. Zbl 1539.65024 Hu, Zheyuan; Shi, Zekun; Karniadakis, George Em; Kawaguchi, Kenji 2 2024 En-DeepONet: an enrichment approach for enhancing the expressivity of neural operators with applications to seismology. Zbl 1539.86005 Haghighat, Ehsan; Waheed, Umair bin; Karniadakis, George 1 2024 Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons. Zbl 07652802 Psaros, Apostolos F.; Meng, Xuhui; Zou, Zongren; Guo, Ling; Karniadakis, George Em 26 2023 Reliable extrapolation of deep neural operators informed by physics or sparse observations. Zbl 1539.65157 Zhu, Min; Zhang, Handi; Jiao, Anran; Karniadakis, George Em; Lu, Lu 9 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. 9 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 7 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. 6 2023 High-order methods for hypersonic flows with strong shocks and real chemistry. Zbl 07715240 Peyvan, Ahmad; Shukla, Khemraj; Chan, Jesse; Karniadakis, George 5 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 2 2023 Multifidelity deep operator networks for data-driven and physics-informed problems. Zbl 07748048 Howard, Amanda A.; Perego, Mauro; Karniadakis, George Em; Stinis, Panos 2 2023 A framework based on symbolic regression coupled with eXtended physics-informed neural networks for gray-box learning of equations of motion from data. Zbl 1539.65153 Kiyani, Elham; Shukla, Khemraj; Karniadakis, George Em; Karttunen, Mikko 2 2023 Accelerating gradient descent and Adam via fractional gradients. Zbl 1535.90114 Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em 1 2023 Bi-orthogonal fPINN: a physics-informed neural network method for solving time-dependent stochastic fractional PDEs. Zbl 1532.65066 Ma, Lei; Li, Rongxin; Zeng, Fanhai; Guo, Ling; Karniadakis, George Em 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 79 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 63 2022 Error estimates for deeponets: a deep learning framework in infinite dimensions. Zbl 07525076 Lanthaler, Samuel; Mishra, Siddhartha; Karniadakis, George E. 49 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 39 2022 Physics-informed neural networks for inverse problems in supersonic flows. Zbl 07561079 Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus; Karniadakis, George Em 28 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 22 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 19 2022 When do extended physics-informed neural networks (XPINNs) improve generalization? Zbl 1498.65183 Hu, Zheyuan; Jagtap, Ameya D.; Karniadakis, George Em; Kawaguchi, Kenji 19 2022 Meta-learning PINN loss functions. Zbl 07527733 Psaros, Apostolos F.; Kawaguchi, Kenji; Karniadakis, George Em 18 2022 Approximation rates of DeepONets for learning operators arising from advection-diffusion equations. Zbl 07751473 Deng, Beichuan; Shin, Yeonjong; Lu, Lu; Zhang, Zhongqiang; Karniadakis, George Em 14 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 13 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 9 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. 6 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 3 2022 A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. Zbl 1531.65019 Zhao, Yue; Mao, Zhiping; Guo, Ling; Tang, Yifa; Karniadakis, George Em 3 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 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 276 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 141 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 105 2021 hp-VPINNs: variational physics-informed neural networks with domain decomposition. Zbl 1506.68105 Kharazmi, Ehsan; Zhang, Zhongqiang; Karniadakis, George E. M. 103 2021 Parallel physics-informed neural networks via domain decomposition. Zbl 07516435 Shukla, Khemraj; Jagtap, Ameya D.; Karniadakis, George Em 53 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 35 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 33 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 31 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 26 2021 Multi-fidelity Bayesian neural networks: algorithms and applications. Zbl 07505956 Meng, Xuhui; Babaee, Hessam; Karniadakis, George Em 26 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 23 2021 Towards a unified theory of fractional and nonlocal vector calculus. Zbl 1498.26008 D’Elia, Marta; Gulian, Mamikon; Olson, Hayley; Karniadakis, George Em 23 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 23 2021 Learning and meta-learning of stochastic advection-diffusion-reaction systems from sparse measurements. Zbl 1538.68040 Chen, Xiaoli; Duan, Jinqiao; 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 A seamless multiscale operator neural network for inferring bubble dynamics. Zbl 1495.76119 Lin, Chensen; Maxey, Martin; Li, Zhen; Karniadakis, George Em 12 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 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. 2 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 Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Zbl 1478.76057 Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em. 200 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 192 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 168 2020 Physics-informed neural networks for high-speed flows. Zbl 1442.76092 Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em 152 2020 Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Zbl 1542.65182 Jagtap, Ameya D.; Karniadakis, George Em 145 2020 Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Zbl 1453.68165 Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em 135 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 93 2020 Physics-informed generative adversarial networks for stochastic differential equations. Zbl 1440.60065 Yang, Liu; Zhang, Dongkun; Karniadakis, George Em 74 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 72 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 70 2020 PPINN: parareal physics-informed neural network for time-dependent PDEs. Zbl 1506.65181 Meng, Xuhui; Li, Zhen; Zhang, Dongkun; Karniadakis, George Em 66 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 51 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. 48 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 43 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 29 2020 Dying ReLU and initialization: theory and numerical examples. Zbl 1507.68248 Lu, Lu; Shin, Yeonjong; Su, Yanhui; Karniadakis, George Em 13 2020 Physics-informed semantic inpainting: application to geostatistical modeling. Zbl 07507237 Zheng, Qiang; Zeng, Lingzao; Karniadakis, George Em 10 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 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 7 2020 Fractional calculus and numerical methods for fractional PDEs. Zbl 1442.35514 Kharazmi, Ehsan; Mao, Zhiping; Pang, Guofei; Zayernouri, Mohsen; Karniadakis, George Em 3 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. 1,362 2019 FPINNs: fractional physics-informed neural networks. Zbl 1420.35459 Pang, Guofei; Lu, Lu; Karniadakis, George Em 195 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 111 2019 Deep learning of vortex-induced vibrations. Zbl 1415.76177 Raissi, Maziar; Wang, Zhicheng; Triantafyllou, Michael S.; Karniadakis, George Em 59 2019 Efficient multistep methods for tempered fractional calculus: algorithms and simulations. Zbl 07099350 Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em 34 2019 Fractional Gray-Scott model: well-posedness, discretization, and simulations. Zbl 1440.35344 Wang, Tingting; Song, Fangying; Wang, Hong; Karniadakis, George Em 19 2019 Neural-net-induced Gaussian process regression for function approximation and PDE solution. Zbl 1451.68242 Pang, Guofei; Yang, Liu; Karniadakis, George Em 18 2019 Machine learning of space-fractional differential equations. Zbl 1419.35209 Gulian, Mamikon; Raissi, Maziar; Perdikaris, Paris; Karniadakis, George 17 2019 Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations. Zbl 1440.65258 Zhao, Tinggang; Mao, Zhiping; Karniadakis, George Em 17 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 12 2019 Numerical methods. Zbl 1410.65001 11 2019 Nonlocal flocking dynamics: learning the fractional order of PDEs from particle simulations. Zbl 1449.35447 Mao, Zhiping; Li, Zhen; Karniadakis, George Em 9 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 7 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 6 2019 Fractional magneto-hydrodynamics: algorithms and applications. Zbl 1416.76127 Song, Fangying; Karniadakis, George Em 5 2019 A Computational Mechanics special issue on: Data-driven modeling and simulation – theory, methods, and applications. Zbl 1476.00073 5 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 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 5 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 Parametric Gaussian process regression for big data. Zbl 1471.62272 Raissi, Maziar; Babaee, Hessam; Karniadakis, George Em 2 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 Hidden physics models: machine learning of nonlinear partial differential equations. Zbl 1381.68248 Raissi, Maziar; Karniadakis, George Em 256 2018 ...and 235 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 11,955 Authors 247 Karniadakis, George Em 81 Sherwin, Spencer J. 68 Wang, Hong 62 Lin, Guang 53 Kirby, Robert M. II 53 Zheng, Xiangcheng 44 Xiu, Dongbin 39 Dong, Suchuan 37 Rozza, Gianluigi 35 Doostan, Alireza 35 Liu, Fawang 34 Narayan, Akil C. 34 Schwab, Christoph 33 Dehghan Takht Fooladi, Mehdi 33 Thompson, Mark Christopher 32 Li, Hong 31 Liu, Yang 31 Shen, Jie 30 Zhou, Tao 29 Hesthaven, Jan S. 29 Perdikaris, Paris G. 28 Venturi, Daniele 28 Zaky, Mahmoud A. 27 Dumbser, Michael 27 Jiang, Xiaoyun 27 Zeng, Fanhai 26 Ghanem, Roger G. 26 Shu, Chi-Wang 26 Zhang, Zhimin 25 Gassner, Gregor J. 25 Kevrekidis, Ioannis George 25 Mishra, Siddhartha 25 Zhang, Zhongqiang 24 Baccouch, Mahboub 24 D’Elia, Marta 24 Kopriva, David Alan 24 Mao, Zhiping 24 Xu, Chuanju 24 Zayernouri, Mohsen 23 Tartakovsky, Daniel M. 23 Yu, Yue 22 Ferrer, Esteban 22 Hourigan, Kerry 22 Jin, Shi 22 Zabaras, Nicholas J. 21 Abbaszadeh, Mostafa 21 Blackburn, Hugh M. 21 Quarteroni, Alfio M. 21 Tartakovsky, Alexandre M. 21 Wan, Xiaoliang 21 Wang, Lilian 20 Knio, Omar M. 20 Lucor, Didier 20 Machado, José António Tenreiro 20 Nobile, Fabio 20 Turner, Ian William 20 Warburton, Timothy 20 Zhang, Dongxiao 19 Brunton, Steven L. 19 Gunzburger, Max Donald 19 Iaccarino, Gianluca 19 Jakeman, John Davis 19 Jornet, Marc 19 Le Maître, Olivier P. 19 Li, Dongfang 19 Li, Zhen 19 Manzoni, Andrea 19 Peiró, Joaquim 19 Tang, Yifa 19 Yang, Xiu 18 Chen, Yong 18 Cortés López, Juan Carlos 18 Guo, Ben-Yu 18 Guo, Ling 18 Pasquetti, Richard 18 Sagaut, Pierre 18 Xing, Yulong 18 Zhang, Zhiwen 17 Ainsworth, Mark 17 Cao, Wanrong 17 Deng, Weihua 17 Duan, Jinqiao 17 Giraldo, Francis X. 17 Kutz, J. Nathan 17 Lu, Lu 17 Nordström, Jan 17 Seaïd, Mohammed 17 Yan, Zhenya 16 Băleanu, Dumitru I. 16 Cheng, Liang 16 Kronbichler, Martin 16 Liu, Wing Kam 16 Luo, Hong 16 Matthies, Hermann Georg 16 Melenk, Jens Markus 16 Moxey, David 16 Najm, Habib N. 16 Noack, Bernd R. 16 Rubio, Gonzalo 16 Soize, Christian ...and 11,855 more Authors all top 5 Cited in 442 Serials 1,421 Journal of Computational Physics 793 Computer Methods in Applied Mechanics and Engineering 382 Journal of Scientific Computing 339 Journal of Fluid Mechanics 328 Computers and Fluids 234 SIAM Journal on Scientific Computing 219 Computers & Mathematics with Applications 183 International Journal for Numerical Methods in Engineering 172 Journal of Computational and Applied Mathematics 153 Applied Numerical Mathematics 128 Physics of Fluids 119 Applied Mathematics and Computation 104 International Journal for Numerical Methods in Fluids 96 Communications in Nonlinear Science and Numerical Simulation 93 Applied Mathematical Modelling 92 SIAM/ASA Journal on Uncertainty Quantification 87 Communications in Computational Physics 84 Computational Mechanics 79 Physica D 78 Mathematics and Computers in Simulation 68 Numerical Methods for Partial Differential Equations 63 Mathematical Methods in the Applied Sciences 60 Numerical Algorithms 58 Computer Physics Communications 58 Mathematics of Computation 58 European Journal of Mechanics. 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