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Picture for George Em Karniadakis

A Caputo fractional derivative-based algorithm for optimization


Apr 06, 2021
Yeonjong Shin, Jérôme Darbon, George Em Karniadakis


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Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates


Jan 17, 2021
Liu Yang, Tingwei Meng, George Em Karniadakis


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Multi-fidelity Bayesian Neural Networks: Algorithms and Applications


Dec 19, 2020
Xuhui Meng, Hessam Babaee, George Em Karniadakis

* 31 pages, 11 figures 

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Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks


Dec 05, 2020
Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis


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Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging


Sep 02, 2020
Enrui Zhang, Minglang Yin, George Em Karniadakis

* 10 pages, 3 figures 

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Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks


Aug 24, 2020
Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis

* The first two authors contributed equally to this paper. Corresponding author: George Em Karniadakis 

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Generative Ensemble-Regression: Learning Stochastic Dynamics from Discrete Particle Ensemble Observations


Aug 05, 2020
Liu Yang, Constantinos Daskalakis, George Em Karniadakis


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Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks


May 07, 2020
Khemraj Shukla, Patricio Clark Di Leoni, James Blackshire, Daniel Sparkman, George Em Karniadakis

* 19 pages, 12 Figures 

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On the Convergence and generalization of Physics Informed Neural Networks


Apr 03, 2020
Yeonjong Shin, Jerome Darbon, George Em Karniadakis


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B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data


Mar 13, 2020
Liu Yang, Xuhui Meng, George Em Karniadakis

* The first two authors contributed equally to this work 

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hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition


Mar 11, 2020
Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis


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Reinforcement Learning for Active Flow Control in Experiments


Mar 06, 2020
Dixia Fan, Liu Yang, Michael S Triantafyllou, George Em Karniadakis

* The first two authors contributed equally to this work 

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Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems


Jan 11, 2020
Pengzhan Jin, Aiqing Zhu, George Em Karniadakis, Yifa Tang


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Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks


Oct 18, 2019
Ameya D. Jagtap, Kenji Kawaguchi, George Em Karniadakis

* 19 pages, 13 figures 

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DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators


Oct 08, 2019
Lu Lu, Pengzhan Jin, George Em Karniadakis


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PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs


Sep 23, 2019
Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis

* 17 pages, 7 figures, 5 tables 

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Physics-informed semantic inpainting: Application to geostatistical modeling


Sep 19, 2019
Qiang Zheng, Lingzao Zeng, George Em Karniadakis


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Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models


Aug 29, 2019
Liu Yang, George Em Karniadakis


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Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks


Jul 23, 2019
Yeonjong Shin, George Em Karniadakis


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Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness


May 27, 2019
Pengzhan Jin, Lu Lu, Yifa Tang, George Em Karniadakis


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


May 03, 2019
Dongkun Zhang, Ling Guo, George Em Karniadakis


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Dying ReLU and Initialization: Theory and Numerical Examples


Mar 15, 2019
Lu Lu, Yeonjong Shin, Yanhui Su, George Em Karniadakis


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Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations


Nov 05, 2018
Liu Yang, Dongkun Zhang, George Em Karniadakis


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Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations


Oct 30, 2018
Zhiping Mao, Zhen Li, George Em Karniadakis

* 22 pages, 7 figures 

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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems


Sep 21, 2018
Dongkun Zhang, Lu Lu, Ling Guo, George Em Karniadakis


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Deep Learning of Vortex Induced Vibrations


Aug 26, 2018
Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou, George Em Karniadakis

* arXiv admin note: text overlap with arXiv:1808.04327 

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Collapse of Deep and Narrow Neural Nets


Aug 15, 2018
Lu Lu, Yanhui Su, George Em Karniadakis


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Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data


Aug 13, 2018
Maziar Raissi, Alireza Yazdani, George Em Karniadakis


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