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Karniadakis, George Em

Author ID: karniadakis.george-em Recent zbMATH articles by "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
Homepage: https://www.brown.edu/research/projects/crunch/george-karniadakis
External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef
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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
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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

Publications by Year

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
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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
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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. B. Fluids
47 Numerical Methods for Partial Differential Equations
45 SIAM Journal on Numerical Analysis
44 Computer Physics Communications
44 Computational and Applied Mathematics
39 Computational Geosciences
38 Numerische Mathematik
37 Advances in Computational Mathematics
37 Fractional Calculus & Applied Analysis
36 International Journal of Computational Fluid Dynamics
34 Chaos, Solitons and Fractals
34 Engineering Analysis with Boundary Elements
34 Communications on Applied Mathematics and Computation
26 International Journal of Heat and Mass Transfer
26 Mathematical Problems in Engineering
26 Nonlinear Dynamics
26 Multiscale Modeling & Simulation
23 Journal of Mathematical Analysis and Applications
23 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
22 Mathematical Methods in the Applied Sciences
22 International Journal of Computational Methods
21 Advances in Difference Equations
20 Journal of Engineering Mathematics
20 BIT
20 Applied Mathematics Letters
20 AMM. Applied Mathematics and Mechanics. (English Edition)
18 East Asian Journal on Applied Mathematics
17 European Journal of Mechanics. A. Solids
17 Archives of Computational Methods in Engineering
17 Numerical Mathematics: Theory, Methods and Applications
16 Journal of Statistical Physics
16 Advances in Applied Mathematics and Mechanics
15 Journal of Applied Mathematics and Computing
15 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
14 Acta Mechanica
14 Computational Methods in Applied Mathematics
13 SIAM Journal on Applied Dynamical Systems
13 International Journal of Numerical Analysis and Modeling
13 Discrete and Continuous Dynamical Systems. Series S
13 International Journal of Applied and Computational Mathematics
12 Inverse Problems
12 Automatica
12 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
12 Discrete and Continuous Dynamical Systems. Series B
12 Acta Numerica
12 Results in Applied Mathematics
11 Journal of Mathematical Physics
11 ZAMP. Zeitschrift für angewandte Mathematik und Physik
11 Theoretical and Computational Fluid Dynamics
11 Mathematical and Computer Modelling
11 Statistics and Computing
11 Journal of Theoretical Biology
11 Research in the Mathematical Sciences
10 Calcolo
10 Neural Networks
10 Mathematical Modelling of Natural Phenomena
9 Physica A
9 Physics Letters. A
9 Meccanica
9 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
8 Japan Journal of Industrial and Applied Mathematics
8 SIAM Review
8 Fractals
8 Computing and Visualization in Science
8 Chaos
8 Journal of Turbulence
8 Foundations of Computational Mathematics
8 Journal of Computational Acoustics
8 GAMM-Mitteilungen
8 Acta Mechanica Sinica
8 Advances in Mathematical Physics
7 Journal of Mathematical Biology
7 Journal of Differential Equations
7 SIAM Journal on Control and Optimization
7 International Journal of Numerical Methods for Heat & Fluid Flow
7 ETNA. Electronic Transactions on Numerical Analysis
7 Vietnam Journal of Mathematics
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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)
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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)
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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)
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15 General and overarching topics; collections (00-XX)
15 Integral transforms, operational calculus (44-XX)
10 Astronomy and astrophysics (85-XX)
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5 Measure and integration (28-XX)
5 Relativity and gravitational theory (83-XX)
2 History and biography (01-XX)
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1 Abstract harmonic analysis (43-XX)
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