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1

Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

Raissi, M., Perdikaris, P., Karniadakis, G.E.

Journal:

Journal of Computational Physics

Année:

2018

Langue:

english

Fichier:

PDF, 2.23 MB

english, 2018

2

Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations

Raissi, Maziar, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2017

Langue:

english

Fichier:

PDF, 4.23 MB

english, 2017

3

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Raissi, Maziar, Yazdani, Alireza, Karniadakis, George Em

Journal:

Année:

2020

Langue:

english

Fichier:

PDF, 2.80 MB

english, 2020

4

fPINNs: Fractional Physics-Informed Neural Networks

Pang, Guofei, Lu, Lu, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2019

Langue:

english

Fichier:

PDF, 1.14 MB

english, 2019

5

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Jin, Xiaowei, Cai, Shengze, Li, Hui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2020

Fichier:

PDF, 5.39 MB

2020

6

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Xiu, Dongbin, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2002

Langue:

english

Fichier:

PDF, 439 KB

english, 2002

7

[Lecture Notes in Computational Science and Engineering] Discontinuous Galerkin Methods Volume 11 || The Development of Discontinuous Galerkin Methods

Cockburn, Bernardo, Karniadakis, George E., Shu, Chi-Wang

Année:

2000

Langue:

english

Fichier:

PDF, 5.53 MB

english, 2000

8

Deep learning of vortex-induced vibrations

Raissi, Maziar, Wang, Zhicheng, Triantafyllou, Michael S., Karniadakis, George Em

Journal:

Journal of Fluid Mechanics

Année:

2019

Langue:

english

Fichier:

PDF, 699 KB

english, 2019

9

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Yang, Liu, Meng, Xuhui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2020

Fichier:

PDF, 5.31 MB

2020

10

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

Kharazmi, Ehsan, Zhang, Zhongqiang, Karniadakis, George E.M.

Journal:

Computer Methods in Applied Mechanics and Engineering

Année:

2021

Fichier:

PDF, 8.78 MB

2021

11

Modeling of blood flow in arterial trees

Tomer Anor, Leopold Grinberg, Hyoungsu Baek, Joseph R. Madsen, Mahesh V. Jayaraman, George E. Karniadakis

Journal:

Wiley Interdisciplinary Reviews: Systems Biology and Medicine

Année:

2010

Langue:

english

Fichier:

PDF, 689 KB

english, 2010

12

REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

Ali Beskok, George Em Karniadakis,

Journal:

Microscale Thermophysical Engineering

Année:

1999

Langue:

english

Fichier:

PDF, 540 KB

english, 1999

13

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

Jagtap, Ameya D., Kharazmi, Ehsan, Karniadakis, George Em

Journal:

Computer Methods in Applied Mechanics and Engineering

Année:

2020

Fichier:

PDF, 20.94 MB

2020

14

High-order splitting methods for the incompressible Navier-Stokes equations

George Em Karniadakis, Moshe Israeli, Steven A Orszag

Journal:

Journal of Computational Physics

Année:

1991

Langue:

english

Fichier:

PDF, 1.42 MB

english, 1991

15

DNS of flow past a stationary and oscillating cylinder at

S. Dong, G.E. Karniadakis

Journal:

Journal of Fluids and Structures

Année:

2005

Langue:

english

Fichier:

PDF, 696 KB

english, 2005

16

Fractional Sturm–Liouville eigen-problems: Theory and numerical approximation

Zayernouri, Mohsen, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2013

Langue:

english

Fichier:

PDF, 1.44 MB

english, 2013

17

Rarefaction and Compressibility Effects in Gas Microflows

Beskok, Ali, Karniadakis, George Em, Trimmer, William

Journal:

Journal of Fluids Engineering

Année:

1996

Langue:

english

Fichier:

PDF, 1.15 MB

english, 1996

18

[ASME ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference - Honolulu, Hawaii, USA (July 6–10, 2003)] Volume 1: Fora, Parts A, B, C, and D - Vortex-Induced Vibrations of Long Marine Risers in Sheared Flows: DNS Studies

Lucor, Didier, Ma, X., Triantafyllou, M. S., Karniadakis, G. E.

Année:

2003

Langue:

english

Fichier:

PDF, 2.98 MB

english, 2003

19

Spectral/hp Element Methods for Computational Fluid Dynamics || ALGORITHMS FOR INCOMPRESSIBLE FLOWS

Karniadakis, George, Sherwin, Spencer

Année:

2005

Langue:

english

Fichier:

PDF, 115 KB

english, 2005

20

Spectral/hp Element Methods for Computational Fluid Dynamics || FUNDAMENTAL CONCEPTS IN ONE DIMENSION

Karniadakis, George, Sherwin, Spencer

Année:

2005

Langue:

english

Fichier:

PDF, 114 KB

english, 2005

21

Inferring solutions of differential equations using noisy multi-fidelity data

Raissi, Maziar, Perdikaris, Paris, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2017

Langue:

english

Fichier:

PDF, 1.68 MB

english, 2017

22

Parametric Gaussian process regression for big data

Raissi, Maziar, Babaee, Hessam, Karniadakis, George Em

Journal:

Computational Mechanics

Année:

2019

Langue:

english

Fichier:

PDF, 2.02 MB

english, 2019

23

Machine Learning of Space-Fractional Differential Equations

Gulian, Mamikon, Raissi, Maziar, Perdikaris, Paris, Karniadakis, George

Journal:

SIAM Journal on Scientific Computing

Année:

2019

Langue:

english

Fichier:

PDF, 2.36 MB

english, 2019

24

What Is the Fractional Laplacian? A Comparative Review with New Results

Lischke, Anna, Pang, Guofei, Gulian, Mamikon, Song, Fangying, Glusa, Christian, Zheng, Xiaoning, Mao, Zhiping, Cai, Wei, Meerschaert, Mark M., Ainsworth, Mark, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2019

Langue:

english

Fichier:

PDF, 8.51 MB

english, 2019

25

Physics-informed neural networks for high-speed flows

Mao, Zhiping, Jagtap, Ameya D., Karniadakis, George Em

Journal:

Computer Methods in Applied Mechanics and Engineering

Année:

2020

Fichier:

PDF, 3.06 MB

2020

26

A new triangular and tetrahedral basis for high-order (hp) finite element methods

Spencer J. Sherwin, George Em Karniadakis

Journal:

International Journal for Numerical Methods in Engineering

Année:

1995

Langue:

english

Fichier:

PDF, 1.33 MB

english, 1995

27

Equation-free/Galerkin-free POD-assisted computation of incompressible flows

Sirod Sirisup, George Em Karniadakis, Dongbin Xiu, Ioannis G. Kevrekidis

Journal:

Journal of Computational Physics

Année:

2005

Langue:

english

Fichier:

PDF, 1.55 MB

english, 2005

28

Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

Xiaoliang Wan, George Em Karniadakis

Journal:

Journal of Scientific Computing

Année:

2006

Langue:

english

Fichier:

PDF, 133 KB

english, 2006

29

Recent advances in parallel spectral element simulation of unsteady incompressible flows

Paul F. Fischer, Ho Lee-Wing, George E. Karniadakis, Einar M. Rønouist, Anthony T. Patera

Journal:

Computers & Structures

Année:

1988

Langue:

english

Fichier:

PDF, 1.47 MB

english, 1988

30

Sensitivity Analysis of the Shipboard Integrated Power System

PRADYA PREMPRANEERACH, FRANZ S. HOVER, MICHAEL S. TRIANTAFYLLOU, TIMOTHY J. MCCOY, CHRYSSOSTOMOS CHRYSSOSTOMIDIS, GEORGE E. KARNIADAKIS

Journal:

Naval Engineers Journal

Année:

2008

Langue:

english

Fichier:

PDF, 1.34 MB

english, 2008

31

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

Karniadakis, George Em, Triantafyllou, George S.

Journal:

Journal of Fluid Mechanics

Année:

1992

Langue:

english

Fichier:

PDF, 6.12 MB

english, 1992

32

[Lecture Notes in Computational Science and Engineering] Discontinuous Galerkin Methods Volume 11 ||

Cockburn, Bernardo, Karniadakis, George E., Shu, Chi-Wang

Année:

2000

Langue:

english

Fichier:

PDF, 397 KB

english, 2000

33

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

Perdikaris, Paris, Karniadakis, George Em.

Journal:

Annals of Biomedical Engineering

Année:

2014

Langue:

english

Fichier:

PDF, 896 KB

english, 2014

34

Second-order approximations for variable order fractional derivatives: Algorithms and applications

Zhao, Xuan, Sun, Zhi-zhong, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2015

Langue:

english

Fichier:

PDF, 427 KB

english, 2015

35

A phase-field method for 3D simulation of two-phase heat transfer

Zheng, X., Babaee, H., Dong, S., Chryssostomidis, C., Karniadakis, G.E.

Journal:

International Journal of Heat and Mass Transfer

Année:

2015

Langue:

english

Fichier:

PDF, 2.44 MB

english, 2015

36

[IEEE 2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM) - Ischia, Italy (2008.06.11-2008.06.13)] 2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion - Stochastic modeling of integrated power system coupled to hydrodynamics in the all-electric ship

Prempraneerach, P., Kirtley, J., Chryssostomidis, C., Triantafyllou, M.S., Karniadakis, G.E.

Année:

2008

Langue:

english

Fichier:

PDF, 1.10 MB

english, 2008

37

Tempered Fractional Sturm--Liouville EigenProblems

Zayernouri, Mohsen, Ainsworth, Mark, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2015

Langue:

english

Fichier:

PDF, 289 KB

english, 2015

38

111 years of Brownian motion

Bian, Xin, Kim, Changho, Karniadakis, George Em

Journal:

Année:

2016

Langue:

english

Fichier:

PDF, 2.27 MB

english, 2016

39

Spectral/hp Element Methods for Computational Fluid Dynamics || INTRODUCTION

Karniadakis, George, Sherwin, Spencer

Année:

2005

Langue:

english

Fichier:

PDF, 473 KB

english, 2005

40

Machine Learning of Linear Differential Equations using Gaussian Processes

Raissi, Maziar, Perdikaris, Paris, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2017

Langue:

english

Fichier:

PDF, 3.35 MB

english, 2017

41

[Applied Mathematical Sciences] Numerical Methods for Stochastic Partial Differential Equations with White Noise Volume 196 || Numerical schemes for SDEs with time delay using the Wong-Zakai approximation

Zhang, Zhongqiang, Karniadakis, George Em

Année:

2017

Langue:

english

Fichier:

PDF, 788 KB

english, 2017

42

[Applied Mathematical Sciences] Numerical Methods for Stochastic Partial Differential Equations with White Noise Volume 196 || Stochastic collocation methods for differential equations with white noise

Zhang, Zhongqiang, Karniadakis, George Em

Année:

2017

Langue:

english

Fichier:

PDF, 383 KB

english, 2017

43

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

Raissi, Maziar, Perdikaris, Paris, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2018

Langue:

english

Fichier:

PDF, 2.46 MB

english, 2018

44

A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations

Yu, Yue, Bargos, Fabiano F., You, Huaiqian, Parks, Michael L., Bittencourt, Marco L., Karniadakis, George E.

Journal:

Computer Methods in Applied Mechanics and Engineering

Année:

2018

Langue:

english

Fichier:

PDF, 3.29 MB

english, 2018

45

Stochastic Domain Decomposition via Moment Minimization

Zhang, Dongkun, Babaee, Hessam, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2018

Langue:

english

Fichier:

PDF, 3.98 MB

english, 2018

46

Correction to: A computational mechanics special issue on: data-driven modeling and simulation—theory, methods, and applications

Liu, Wing Kam, Karniadakis, George, Tang, Shaoqiang, Yvonnet, Julien

Journal:

Computational Mechanics

Année:

2019

Langue:

english

Fichier:

PDF, 134 KB

english, 2019

47

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Meng, Xuhui, Karniadakis, George Em

Journal:

Journal of Computational Physics

Année:

2019

Fichier:

PDF, 1.26 MB

2019

48

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

Yang, Liu, Zhang, Dongkun, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2020

Fichier:

PDF, 2.69 MB

2020

49

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

Zhang, Dongkun, Guo, Ling, Karniadakis, George Em

Journal:

SIAM Journal on Scientific Computing

Année:

2020

Langue:

english

Fichier:

PDF, 1.87 MB

english, 2020

50

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Meng, Xuhui, Li, Zhen, Zhang, Dongkun, Karniadakis, George Em

Journal:

Computer Methods in Applied Mechanics and Engineering

Année:

2020

Fichier:

PDF, 2.79 MB

2020