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ORCIDGeorge Em Karniadakis
George E. Karniadakis
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- affiliation: Brown University, Division of Applied Mathematics, Providence, RI, USA
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2020 – today
- 2022
[j170]Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis:
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. Neurocomputing 468: 165-180 (2022)- [j169]Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis
, George Em Karniadakis:
Learning functional priors and posteriors from data and physics. J. Comput. Phys. 457: 111073 (2022) - [j168]Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis:
Meta-learning PINN loss functions. J. Comput. Phys. 458: 111121 (2022) - [j167]Khemraj Shukla, Ameya D. Jagtap, James L. Blackshire, Daniel Sparkman, George Em Karniadakis:
A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems. IEEE Signal Process. Mag. 39(1): 68-77 (2022) - [j166]Liu Yang, George Em Karniadakis:
Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models. IEEE Trans. Neural Networks Learn. Syst. 33(2): 528-538 (2022) - [i82]Tingwei Meng, Zhen Zhang, Jérôme Darbon, George Em Karniadakis:
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems. CoRR abs/2201.05475 (2022) - [i81]Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis:
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons. CoRR abs/2201.07766 (2022) - [i80]Mitchell Daneker, Zhen Zhang, George Em Karniadakis, Lu Lu:
Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks. CoRR abs/2202.01723 (2022) - [i79]Ameya D. Jagtap, Dimitrios Mitsotakis, George Em Karniadakis:
Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations. CoRR abs/2202.02899 (2022) - [i78]Marta D'Elia, Hang Deng, Cedric G. Fraces, Krishna Garikipati, Lori Graham-Brady, Amanda A. Howard, George Em Karniadakis, Vahid Keshavarzzadeh, Robert M. Kirby, J. Nathan Kutz, Chunhui Li, Xing Liu, Hannah Lu, Pania Newell, Daniel O'Malley, Masa Prodanovic, Gowri Srinivasan, Alexandre M. Tartakovsky, Daniel M. Tartakovsky, Hamdi A. Tchelepi, Bozo Vazic, Hari S. Viswanathan, Hongkyu Yoon, Piotr Zarzycki:
Machine Learning in Heterogeneous Porous Materials. CoRR abs/2202.04137 (2022) - [i77]Ameya D. Jagtap, Zhiping Mao, Nikolaus Adams, George Em Karniadakis:
Physics-informed neural networks for inverse problems in supersonic flows. CoRR abs/2202.11821 (2022) - [i76]Minglang Yin, Enrui Zhang, Yue Yu, George Em Karniadakis:
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems. CoRR abs/2203.00003 (2022) - [i75]Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis:
On the influence of over-parameterization in manifold based surrogates and deep neural operators. CoRR abs/2203.05071 (2022) - [i74]Ethan Pickering, George Em Karniadakis, Themistoklis P. Sapsis:
Discovering and forecasting extreme events via active learning in neural operators. CoRR abs/2204.02488 (2022) - [i73]Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Rémi Dingreville, George Em Karniadakis:
Learning two-phase microstructure evolution using neural operators and autoencoder architectures. CoRR abs/2204.07230 (2022) - [i72]Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis:
Multifidelity Deep Operator Networks. CoRR abs/2204.09157 (2022) - [i71]Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis:
Deep transfer learning for partial differential equations under conditional shift with DeepONet. CoRR abs/2204.09810 (2022) - [i70]Somdatta Goswami, David S. Li, Bruno V. Rego, Marcos Latorre, Jay D. Humphrey, George Em Karniadakis:
Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms. CoRR abs/2205.03780 (2022) - [i69]Kevin Linka, Amelie Schafer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl:
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems. CoRR abs/2205.08304 (2022) - [i68]Khemraj Shukla, Mengjia Xu, Nathaniel Trask, George Em Karniadakis:
Scalable algorithms for physics-informed neural and graph networks. CoRR abs/2205.08332 (2022) - [i67]Adar Kahana, Qian Zhang, Leonard Gleyzer, George Em Karniadakis:
Function Regression using Spiking DeepONet. CoRR abs/2205.10130 (2022) - 2021
- [j165]Max Carlson, Xiaoning Zheng, Hari Sundar, George Em Karniadakis, Robert M. Kirby:
An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains. Comput. Phys. Commun. 261: 107695 (2021) - [j164]Fangying Song, George Em Karniadakis:
Variable-Order Fractional Models for Wall-Bounded Turbulent Flows. Entropy 23(6): 782 (2021) - [j163]Liu Yang, Xuhui Meng, George Em Karniadakis:
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. J. Comput. Phys. 425: 109913 (2021) - [j162]Xiaowei Jin, Shengze Cai, Hui Li, George Em Karniadakis:
NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations. J. Comput. Phys. 426: 109951 (2021) - [j161]Lifei Zhao, Zhen Li, Zhicheng Wang, Bruce Caswell, Jie Ouyang, George Em Karniadakis:
Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows. J. Comput. Phys. 427: 110069 (2021) - [j160]Zhicheng Wang, Xiaoning Zheng, Chryssostomos Chryssostomidis, George Em Karniadakis:
A phase-field method for boiling heat transfer. J. Comput. Phys. 435: 110239 (2021) - [j159]Shengze Cai, Zhicheng Wang, Lu Lu, Tamer A. Zaki, George Em Karniadakis:
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks. J. Comput. Phys. 436: 110296 (2021) - [j158]Xuhui Meng, Hessam Babaee, George Em Karniadakis:
Multi-fidelity Bayesian neural networks: Algorithms and applications. J. Comput. Phys. 438: 110361 (2021) - [j157]Qin Lou, Xuhui Meng, George Em Karniadakis:
Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. J. Comput. Phys. 447: 110676 (2021) - [j156]Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis:
Parallel physics-informed neural networks via domain decomposition. J. Comput. Phys. 447: 110683 (2021) - [j155]Zhiping Mao, Lu Lu, Olaf Marxen, Tamer A. Zaki, George Em Karniadakis:
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. J. Comput. Phys. 447: 110698 (2021) - [j154]Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, George Em Karniadakis:
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3(3): 218-229 (2021) - [j153]Sheng Zhang, Joan Ponce, Zhen Zhang, Guang Lin, George E. Karniadakis:
An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City. PLoS Comput. Biol. 17(9) (2021) - [j152]He Li, Zixiang Leonardo Liu, Lu Lu, Pierre Buffet, George Em Karniadakis:
How the spleen reshapes and retains young and old red blood cells: A computational investigation. PLoS Comput. Biol. 17(11) (2021) - [j151]Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis:
DeepXDE: A Deep Learning Library for Solving Differential Equations. SIAM Rev. 63(1): 208-228 (2021) - [j150]Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis:
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-Informed Neural Networks. SIAM J. Sci. Comput. 43(3): B811-B830 (2021) - [c25]Ameya D. Jagtap, George E. Karniadakis:
Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations. AAAI Spring Symposium: MLPS 2021 - [i66]Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis:
Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation. CoRR abs/2101.02355 (2021) - [i65]Liu Yang, Tingwei Meng, George Em Karniadakis:
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates. CoRR abs/2101.06802 (2021) - [i64]Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis:
Error estimates for DeepOnets: A deep learning framework in infinite dimensions. CoRR abs/2102.09618 (2021) - [i63]Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis:
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations. CoRR abs/2102.10621 (2021) - [i62]Yeonjong Shin, Jérôme Darbon, George Em Karniadakis:
A Caputo fractional derivative-based algorithm for optimization. CoRR abs/2104.02259 (2021) - [i61]Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis:
Parallel Physics-Informed Neural Networks via Domain Decomposition. CoRR abs/2104.10013 (2021) - [i60]Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, George Em Karniadakis:
Physics-informed neural networks (PINNs) for fluid mechanics: A review. CoRR abs/2105.09506 (2021) - [i59]Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis:
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. CoRR abs/2105.09513 (2021) - [i58]Qian Zhang, Konstantina Sampani, Mengjia Xu, Shengze Cai, Yixiang Deng, He Li, Jennifer K. Sun, George Em Karniadakis:
AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images. CoRR abs/2106.02800 (2021) - [i57]Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis, George Em Karniadakis:
Learning Functional Priors and Posteriors from Data and Physics. CoRR abs/2106.05863 (2021) - [i56]Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis:
Meta-learning PINN loss functions. CoRR abs/2107.05544 (2021) - [i55]Somdatta Goswami, Minglang Yin, Yue Yu, George E. Karniadakis:
A physics-informed variational DeepONet for predicting the crack path in brittle materials. CoRR abs/2108.06905 (2021) - [i54]Minglang Yin, Ehsan Ban, Bruno V. Rego, Enrui Zhang, Cristina Cavinato, Jay D. Humphrey, George Em Karniadakis:
Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network. CoRR abs/2108.11985 (2021) - [i53]Zhen Zhang, Yeonjong Shin, George Em Karniadakis:
GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems. CoRR abs/2109.00092 (2021) - [i52]Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi:
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? CoRR abs/2109.09444 (2021) - [i51]Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis:
DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs. CoRR abs/2109.13441 (2021) - [i50]Jeremy Yu, Lu Lu, Xuhui Meng, George Em Karniadakis:
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. CoRR abs/2111.02801 (2021) - 2020
- [j149]Xuhui Meng, George Em Karniadakis:
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. J. Comput. Phys. 401 (2020) - [j148]Ameya D. Jagtap, Kenji Kawaguchi, George Em Karniadakis:
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. J. Comput. Phys. 404 (2020) - [j147]Anna Lischke, Guofei Pang, Mamikon A. Gulian, Fangying Song, Christian A. Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis:
What is the fractional Laplacian? A comparative review with new results. J. Comput. Phys. 404 (2020) - [j146]Hui Zhang, Xiaoyun Jiang, Fanhai Zeng, George Em Karniadakis:
A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations. J. Comput. Phys. 405: 109141 (2020) - [j145]Qiang Zheng, Lingzao Zeng, George Em Karniadakis:
Physics-informed semantic inpainting: Application to geostatistical modeling. J. Comput. Phys. 419: 109676 (2020) - [j144]Guofei Pang, Marta D'Elia, Michael L. Parks, George E. Karniadakis:
nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. J. Comput. Phys. 422: 109760 (2020) - [j143]Pengzhan Jin, Lu Lu, Yifa Tang, George Em Karniadakis:
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. Neural Networks 130: 85-99 (2020) - [j142]Pengzhan Jin, Zhen Zhang, Aiqing Zhu, Yifa Tang, George Em Karniadakis:
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Networks 132: 166-179 (2020) - [j141]Xiaoning Zheng, Alireza Yazdani, He Li, Jay D. Humphrey, George E. Karniadakis:
A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels. PLoS Comput. Biol. 16(4) (2020) - [j140]Alireza Yazdani, Lu Lu, Maziar Raissi, George Em Karniadakis:
Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput. Biol. 16(11) (2020) - [j139]Liu Yang, Dongkun Zhang, George Em Karniadakis:
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. SIAM J. Sci. Comput. 42(1): A292-A317 (2020) - [j138]Dongkun Zhang, Ling Guo, George Em Karniadakis:
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. SIAM J. Sci. Comput. 42(2): A639-A665 (2020) - [c24]Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis:
DeepXDE: A Deep Learning Library for Solving Differential Equations. AAAI Spring Symposium: MLPS 2020 - [c23]Marta D'Elia, George E. Karniadakis, Guofei Pang, Michael L. Parks:
Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models. AAAI Spring Symposium: MLPS 2020 - [i49]Pengzhan Jin, Aiqing Zhu, George Em Karniadakis, Yifa Tang:
Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems. CoRR abs/2001.03750 (2020) - [i48]Dixia Fan, Liu Yang, Michael S. Triantafyllou, George Em Karniadakis:
Reinforcement Learning for Active Flow Control in Experiments. CoRR abs/2003.03419 (2020) - [i47]Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis:
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition. CoRR abs/2003.05385 (2020) - [i46]Liu Yang, Xuhui Meng, George Em Karniadakis:
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data. CoRR abs/2003.06097 (2020) - [i45]Yeonjong Shin, Jérôme Darbon, George Em Karniadakis:
On the Convergence and generalization of Physics Informed Neural Networks. CoRR abs/2004.01806 (2020) - [i44]Guofei Pang, Marta D'Elia, Michael L. Parks, George E. Karniadakis:
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications. CoRR abs/2004.04276 (2020) - [i43]Khemraj Shukla, Patricio Clark Di Leoni, James L. Blackshire, Daniel Sparkman, George Em Karniadakis:
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks. CoRR abs/2005.03596 (2020) - [i42]Hui Zhang, Fanhai Zeng, Xiaoyun Jiang, George Em Karniadakis:
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. CoRR abs/2007.07015 (2020) - [i41]Liu Yang, Constantinos Daskalakis, George Em Karniadakis:
Generative Ensemble-Regression: Learning Stochastic Dynamics from Discrete Particle Ensemble Observations. CoRR abs/2008.01915 (2020) - [i40]Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis:
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks. CoRR abs/2008.10653 (2020) - [i39]Enrui Zhang, Minglang Yin, George Em Karniadakis:
Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging. CoRR abs/2009.04525 (2020) - [i38]Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis:
Error estimates of residual minimization using neural networks for linear PDEs. CoRR abs/2010.08019 (2020) - [i37]Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis:
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks. CoRR abs/2012.03133 (2020) - [i36]Xuhui Meng, Hessam Babaee, George Em Karniadakis:
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications. CoRR abs/2012.13294 (2020)
2010 – 2019
- 2019
- [j137]Fangying Song, George E. Karniadakis:
Fractional magneto-hydrodynamics: Algorithms and applications. J. Comput. Phys. 378: 44-62 (2019) - [j136]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378: 686-707 (2019) - [j135]Guofei Pang, Liu Yang, George E. Karniadakis:
Neural-net-induced Gaussian process regression for function approximation and PDE solution. J. Comput. Phys. 384: 270-288 (2019) - [j134]Ansel L. Blumers, Zhen Li, George E. Karniadakis:
Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics. J. Comput. Phys. 393: 214-228 (2019) - [j133]Zhicheng Wang, Suchuan Dong, Michael S. Triantafyllou, Yiannis Constantinides, George Em Karniadakis:
A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio. J. Comput. Phys. 397 (2019) - [j132]Dongkun Zhang, Lu Lu, Ling Guo, George Em Karniadakis:
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. J. Comput. Phys. 397 (2019) - [j131]Dixia Fan, Gurvan Jodin, Thomas Consi, L. Bonfiglio, Y. Ma, Elizabeth Keyes, George E. Karniadakis, Michael S. Triantafyllou:
A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics. Sci. Robotics 4(36) (2019) - [j130]Nan Wang, Zhiping Mao, Chengming Huang, George E. Karniadakis:
A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions. SIAM J. Sci. Comput. 41(3): A1840-A1866 (2019) - [j129]Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Machine Learning of Space-Fractional Differential Equations. SIAM J. Sci. Comput. 41(4): A2485-A2509 (2019) - [j128]Ling Guo, Fanhai Zeng, Ian W. Turner, Kevin Burrage, George Em Karniadakis:
Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations. SIAM J. Sci. Comput. 41(4): A2510-A2535 (2019) - [j127]Guofei Pang, Lu Lu, George Em Karniadakis:
fPINNs: Fractional Physics-Informed Neural Networks. SIAM J. Sci. Comput. 41(4): A2603-A2626 (2019) - [c22]Liu Yang, Prabhat, George E. Karniadakis, Sean Treichler, Thorsten Kurth, Keno Fischer, David A. Barajas-Solano, Joshua Romero, Valentin Churavy, Alexandre M. Tartakovsky, Michael Houston:
Highly-Ccalable, Physics-Informed GANs for Learning Solutions of Stochastic PDEs. DLS@SC 2019: 1-11 - [i35]Lu Lu, Yeonjong Shin, Yanhui Su, George E. Karniadakis:
Dying ReLU and Initialization: Theory and Numerical Examples. CoRR abs/1903.06733 (2019) - [i34]Dongkun Zhang, Ling Guo, George E. Karniadakis:
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. CoRR abs/1905.01205 (2019) - [i33]Pengzhan Jin, Lu Lu, Yifa Tang, George E. Karniadakis:
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. CoRR abs/1905.11427 (2019) - [i32]Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis:
DeepXDE: A deep learning library for solving differential equations. CoRR abs/1907.04502 (2019) - [i31]Yeonjong Shin, George E. Karniadakis:
Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks. CoRR abs/1907.09696 (2019) - [i30]Liu Yang, George E. Karniadakis:
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models. CoRR abs/1908.11462 (2019) - [i29]Qiang Zheng, Lingzao Zeng, George E. Karniadakis:
Physics-informed semantic inpainting: Application to geostatistical modeling. CoRR abs/1909.09459 (2019) - [i28]Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis:
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs. CoRR abs/1909.10145 (2019) - [i27]Ameya D. Jagtap, Kenji Kawaguchi, George E. Karniadakis:
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks. CoRR abs/1909.12228 (2019) - [i26]Lu Lu, Pengzhan Jin, George Em Karniadakis:
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. CoRR abs/1910.03193 (2019) - [i25]Xiaoli Chen, Jinqiao Duan, George Em Karniadakis:
Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements. CoRR abs/1910.09098 (2019) - [i24]Liu Yang, Sean Treichler, Thorsten Kurth, Keno Fischer, David A. Barajas-Solano, Joshua Romero, Valentin Churavy, Alexandre M. Tartakovsky, Michael Houston, Prabhat, George E. Karniadakis:
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs. CoRR abs/1910.13444 (2019) - [i23]Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis:
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations. CoRR abs/1912.00873 (2019) - [i22]José del Águila Ferrandis, Michael S. Triantafyllou, Chryssostomos Chryssostomidis, George Em Karniadakis:
Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states. CoRR abs/1912.13382 (2019) - 2018
- [j126]Zhen Li, Xin Bian, Yu-Hang Tang, George E. Karniadakis:
A dissipative particle dynamics method for arbitrarily complex geometries. J. Comput. Phys. 355: 534-547 (2018) - [j125]Maziar Raissi, George E. Karniadakis:
Hidden physics models: Machine learning of nonlinear partial differential equations. J. Comput. Phys. 357: 125-141 (2018) - [j124]Lifei Zhao, Zhen Li, Bruce Caswell, Jie Ouyang, George E. Karniadakis:
Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. J. Comput. Phys. 363: 116-127 (2018) - [j123]Dongkun Zhang, Liu Yang, George E. Karniadakis:
Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors. J. Comput. Phys. 374: 121-134 (2018) - [j122]Zhiping Mao, George E. Karniadakis:
A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative. SIAM J. Numer. Anal. 56(1): 24-49 (2018) - [j121]Zhijiang Zhang, Weihua Deng, George E. Karniadakis:
A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian. SIAM J. Numer. Anal. 56(5): 3010-3039 (2018) - [j120]