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ORCIDGeorge E. Karniadakis
George Em Karniadakis
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- affiliation: Brown University, Division of Applied Mathematics, Providence, RI, USA
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2020 – today
- 2021
[j151]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)- [j150]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) - [j149]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) - [i53]Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis:
Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation. CoRR abs/2101.02355 (2021) - [i52]Liu Yang, Tingwei Meng, George Em Karniadakis:
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates. CoRR abs/2101.06802 (2021) - [i51]Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis:
Error estimates for DeepOnets: A deep learning framework in infinite dimensions. CoRR abs/2102.09618 (2021) - [i50]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) - 2020
- [j148]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) - [j147]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) - [j146]Anna Lischke, Guofei Pang, Mamikon A. Gulian, Fangying Song, Christian 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) - [j145]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) - [j144]Qiang Zheng, Lingzao Zeng, George Em Karniadakis:
Physics-informed semantic inpainting: Application to geostatistical modeling. J. Comput. Phys. 419: 109676 (2020) - [j143]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) - [j142]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) - [j141]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) - [j140]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) - [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) - [c23]Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis:
DeepXDE: A Deep Learning Library for Solving Differential Equations. AAAI Spring Symposium: MLPS 2020 - [c22]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 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) - [c21]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]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations. SIAM J. Sci. Comput. 40(1) (2018) - [j119]Ivi C. Tsantili, Min Hyung Cho, Wei Cai, George E. Karniadakis:
A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints. SIAM J. Sci. Comput. 40(2) (2018) - [j118]Dongkun Zhang, Hessam Babaee, George E. Karniadakis:
Stochastic Domain Decomposition via Moment Minimization. SIAM J. Sci. Comput. 40(4): A2152-A2173 (2018) - [j117]Fanhai Zeng, Ian W. Turner, Kevin Burrage, George E. Karniadakis:
A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations. SIAM J. Sci. Comput. 40(5): A2986-A3011 (2018) - [i21]Guofei Pang, Liu Yang, George E. Karniadakis:
Neural-net-induced Gaussian process regression for function approximation and PDE solution. CoRR abs/1806.11187 (2018) - [i20]Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Machine Learning of Space-Fractional Differential Equations. CoRR abs/1808.00931 (2018) - [i19]Maziar Raissi, Alireza Yazdani, George E. Karniadakis:
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data. CoRR abs/1808.04327 (2018) - [i18]Lu Lu, Yanhui Su, George E. Karniadakis:
Collapse of Deep and Narrow Neural Nets. CoRR abs/1808.04947 (2018) - [i17]Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou, George E. Karniadakis:
Deep Learning of Vortex Induced Vibrations. CoRR abs/1808.08952 (2018) - [i16]Liu Yang, Dongkun Zhang, George E. Karniadakis:
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. CoRR abs/1811.02033 (2018) - [i15]Seungjoon Lee, Felix Dietrich, George E. Karniadakis, Ioannis G. Kevrekidis:
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion. CoRR abs/1812.06467 (2018) - 2017
- [j116]Fangying Song, Fanhai Zeng, Wei Cai, Wen Chen, George E. Karniadakis:
Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes. Comput. Math. Appl. 73(6): 1286-1297 (2017) - [j115]Ansel L. Blumers, Yu-Hang Tang, Zhen Li, Xuejin Li, George E. Karniadakis:
GPU-accelerated red blood cells simulations with transport dissipative particle dynamics. Comput. Phys. Commun. 217: 171-179 (2017) - [j114]Huan Lei, Xiu Yang, Zhen Li, George E. Karniadakis:
Systematic parameter inference in stochastic mesoscopic modeling. J. Comput. Phys. 330: 571-593 (2017) - [j113]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Inferring solutions of differential equations using noisy multi-fidelity data. J. Comput. Phys. 335: 736-746 (2017) - [j112]Lucia Parussini, Daniele Venturi, Paris Perdikaris, George E. Karniadakis:
Multi-fidelity Gaussian process regression for prediction of random fields. J. Comput. Phys. 336: 36-50 (2017) - [j111]Zhiping Mao, George E. Karniadakis:
Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods. J. Comput. Phys. 336: 143-163 (2017) - [j110]Mingge Deng, Wenxiao Pan, George E. Karniadakis:
Anisotropic single-particle dissipative particle dynamics model. J. Comput. Phys. 336: 481-491 (2017) - [j109]Hessam Babaee, Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis:
A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems. J. Comput. Phys. 344: 303-319 (2017) - [j108]Seungjoon Lee, Ioannis G. Kevrekidis, George E. Karniadakis:
A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion. J. Comput. Phys. 344: 516-533 (2017) - [j107]Seungjoon Lee, Ioannis G. Kevrekidis, George E. Karniadakis:
A general CFD framework for fault-resilient simulations based on multi-resolution information fusion. J. Comput. Phys. 347: 290-304 (2017) - [j106]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Machine learning of linear differential equations using Gaussian processes. J. Comput. Phys. 348: 683-693 (2017) - [j105]Guofei Pang, Paris Perdikaris, Wei Cai, George E. Karniadakis:
Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. J. Comput. Phys. 348: 694-714 (2017) - [j104]Alireza Yazdani, He Li, Jay D. Humphrey, George E. Karniadakis:
A General Shear-Dependent Model for Thrombus Formation. PLoS Comput. Biol. 13(1) (2017) - [j103]Xuejin Li, E. Du, Ming Dao, Subra Suresh, George E. Karniadakis:
Patient-specific modeling of individual sickle cell behavior under transient hypoxia. PLoS Comput. Biol. 13(3) (2017) - [j102]Mengjia Xu, Dimitrios P. Papageorgiou, Sabia Z. Abidi, Ming Dao, Hong Zhao, George E. Karniadakis:
A deep convolutional neural network for classification of red blood cells in sickle cell anemia. PLoS Comput. Biol. 13(10) (2017) - [j101]Fanhai Zeng, Zhiping Mao, George E. Karniadakis:
A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities. SIAM J. Sci. Comput. 39(1) (2017) - [j100]Ehsan Kharazmi, Mohsen Zayernouri, George E. Karniadakis:
Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations. SIAM J. Sci. Comput. 39(3) (2017) - [j99]Anna Lischke, Mohsen Zayernouri, George E. Karniadakis:
A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half Line. SIAM J. Sci. Comput. 39(3) (2017) - [j98]Fangying Song, Chuanju Xu, George E. Karniadakis:
Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations. SIAM J. Sci. Comput. 39(4) (2017) - [i14]Yu-Hang Tang, Lu Lu, He Li, Constantinos Evangelinos, Leopold Grinberg, Vipin Sachdeva, George E. Karniadakis:
OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution. CoRR abs/1701.02059 (2017) - [i13]Maziar Raissi, George E. Karniadakis:
Machine Learning of Linear Differential Equations using Gaussian Processes. CoRR abs/1701.02440 (2017) - [i12]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations. CoRR abs/1703.10230 (2017) - [i11]Maziar Raissi, George E. Karniadakis:
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations. CoRR abs/1708.00588 (2017) - [i10]Yu-Hang Tang, Dongkun Zhang, George E. Karniadakis:
An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields. CoRR abs/1709.09235 (2017) - [i9]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. CoRR abs/1711.10561 (2017) - [i8]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations. CoRR abs/1711.10566 (2017) - 2016
- [j97]Heyrim Cho, Daniele Venturi, George E. Karniadakis:
Numerical methods for high-dimensional probability density function equations. J. Comput. Phys. 305: 817-837 (2016) - [j96]Alireza Yazdani, Mingge Deng, Bruce Caswell, George E. Karniadakis:
Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces. J. Comput. Phys. 305: 906-920 (2016) - [j95]Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis:
Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. J. Comput. Phys. 307: 15-33 (2016) - [j94]Yue Yu, Paris Perdikaris, George E. Karniadakis:
Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. J. Comput. Phys. 323: 219-242 (2016) - [j93]Zhongqiang Zhang, Boris Rozovskii, George E. Karniadakis:
Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise. Numerische Mathematik 134(1): 61-89 (2016) - [j92]Paris Perdikaris, Joseph A. Insley, Leopold Grinberg, Yue Yu, Michael E. Papka, George E. Karniadakis:
Visualizing multiphysics, fluid-structure interaction phenomena in intracranial aneurysms. Parallel Comput. 55: 9-16 (2016) - [j91]Hung-Yu Chang, Xuejin Li, He Li, George E. Karniadakis:
MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease. PLoS Comput. Biol. 12(10) (2016) - [j90]Paris Perdikaris, Daniele Venturi, George E. Karniadakis:
Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets. SIAM J. Sci. Comput. 38(4) (2016) - [j89]Wanrong Cao, Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis:
Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions. SIAM J. Sci. Comput. 38(5) (2016) - [i7]Maziar Raissi, George E. Karniadakis:
Deep Multi-fidelity Gaussian Processes. CoRR abs/1604.07484 (2016) - [i6]Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Inferring solutions of differential equations using noisy multi-fidelity data. CoRR abs/1607.04805 (2016) - 2015
- [j88]George E. Karniadakis, Jan S. Hesthaven, Igor Podlubny:
Special Issue on "Fractional PDEs: Theory, Numerics, and Applications". J. Comput. Phys. 293: 1-3 (2015) - [j87]Xuan Zhao, Zhi-Zhong Sun, George E. Karniadakis:
Second-order approximations for variable order fractional derivatives: Algorithms and applications. J. Comput. Phys. 293: 184-200 (2015) - [j86]Mohsen Zayernouri, George E. Karniadakis:
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. J. Comput. Phys. 293: 312-338 (2015) - [j85]Yu-Hang Tang, Shuhei Kudo, Xin Bian, Zhen Li, George E. Karniadakis:
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers. J. Comput. Phys. 297: 13-31 (2015) - [j84]Xin Bian, Zhen Li, George E. Karniadakis:
Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition. J. Comput. Phys. 297: 132-155 (2015) - [j83]