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George Em Karniadakis
George Em Karniadakis
The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering
Verified email at brown.edu - Homepage
Title
Cited by
Cited by
Year
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M Raissi, P Perdikaris, GE Karniadakis
Journal of Computational physics 378, 686-707, 2019
81312019
The Wiener--Askey polynomial chaos for stochastic differential equations
D Xiu, GE Karniadakis
SIAM journal on scientific computing 24 (2), 619-644, 2002
56202002
Spectral/hp element methods for computational fluid dynamics
G Karniadakis, SJ Sherwin
Oxford University Press, USA, 2005
34722005
Discontinuous Galerkin methods: theory, computation and applications
B Cockburn, GE Karniadakis, CW Shu
Springer Science & Business Media, 2012
2946*2012
Physics-informed machine learning
GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang
Nature Reviews Physics 3 (6), 422-440, 2021
28722021
Microflows and nanoflows: fundamentals and simulation
G Karniadakis, A Beskok, N Aluru
Springer Science & Business Media, 2006
27362006
High-order splitting methods for the incompressible Navier-Stokes equations
GE Karniadakis, M Israeli, SA Orszag
Journal of computational physics 97 (2), 414-443, 1991
17731991
Modeling uncertainty in flow simulations via generalized polynomial chaos
D Xiu, GE Karniadakis
Journal of computational physics 187 (1), 137-167, 2003
17352003
Report: a model for flows in channels, pipes, and ducts at micro and nano scales
A Beskok, GE Karniadakis
Microscale thermophysical engineering 3 (1), 43-77, 1999
14961999
Micro flows: fundamentals and simulation
GE Karniadakis, A Beskok, M Gad-el-Hak
Appl. Mech. Rev. 55 (4), B76-B76, 2002
13742002
DeepXDE: A deep learning library for solving differential equations
L Lu, X Meng, Z Mao, GE Karniadakis
SIAM review 63 (1), 208-228, 2021
13182021
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
M Raissi, A Yazdani, GE Karniadakis
Science 367 (6481), 1026-1030, 2020
12812020
Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations
M Raissi, P Perdikaris, GE Karniadakis
arXiv preprint arXiv:1711.10561, 2017
12102017
Hidden physics models: Machine learning of nonlinear partial differential equations
M Raissi, GE Karniadakis
Journal of Computational Physics 357, 125-141, 2018
11722018
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
L Lu, P Jin, G Pang, Z Zhang, GE Karniadakis
Nature machine intelligence 3 (3), 218-229, 2021
11282021
Physics-informed neural networks for high-speed flows
Z Mao, AD Jagtap, GE Karniadakis
Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020
7422020
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
D Xiu, GE Karniadakis
Computer methods in applied mechanics and engineering 191 (43), 4927-4948, 2002
7292002
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
X Wan, GE Karniadakis
Journal of Computational Physics 209 (2), 617-642, 2005
7262005
NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
X Jin, S Cai, H Li, GE Karniadakis
Journal of Computational Physics 426, 109951, 2021
6822021
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
AD Jagtap, K Kawaguchi, GE Karniadakis
Journal of Computational Physics 404, 109136, 2020
676*2020
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