George E. Karniadakis

ORCID

Publication Activity (10 Years)

Years Active: 1996-2024
Publications (10 Years): 87

Top Venues

Publications

Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George E. Karniadakis
NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators. SIAM Rev. 66 (1) (2024)
Minglei Lu, Chensen Lin, Martian Maxey, George E. Karniadakis, Zhen Li
Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning. CoRR (2024)
Ahmad Peyvan, Khemraj Shukla, Jesse Chan, George E. Karniadakis
High-order methods for hypersonic flows with strong shocks and real chemistry. J. Comput. Phys. 490 (2023)
He Li, Yixiang Deng, Konstantina Sampani, Shengze Cai, Zhen Li, Jennifer K. Sun, George E. Karniadakis
Computational investigation of blood cell transport in retinal microaneurysms. PLoS Comput. Biol. 18 (1) (2022)
Liu Yang, Constantinos Daskalakis, George E. Karniadakis
Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models. SIAM J. Sci. Comput. 44 (1) (2022)
Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis
Multifidelity Deep Operator Networks. CoRR (2022)
Tingwei Meng, Zhen Zhang, Jérôme Darbon, George E. Karniadakis
SympOCnet: Solving Optimal Control Problems with Applications to High-Dimensional Multiagent Path Planning Problems. SIAM J. Sci. Comput. 44 (6) (2022)
He Li, Yixiang Deng, Zhen Li, Ander Dorken Gallastegi, Christos S. Mantzoros, Galit H. Frydman, George E. Karniadakis
Multiphysics and multiscale modeling of microthrombosis in COVID-19. PLoS Comput. Biol. 18 (3) (2022)
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)
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)
Somdatta Goswami, Minglang Yin, Yue Yu, George E. Karniadakis
A physics-informed variational DeepONet for predicting the crack path in brittle materials. CoRR (2021)
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 (2020)
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)
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)
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 (2020)
Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis
DeepXDE: A deep learning library for solving differential equations. CoRR (2019)
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 (2019)
Qiang Zheng, Lingzao Zeng, George E. Karniadakis
Physics-informed semantic inpainting: Application to geostatistical modeling. CoRR (2019)
Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Machine Learning of Space-Fractional Differential Equations. SIAM J. Sci. Comput. 41 (4) (2019)
Guofei Pang, Liu Yang, George E. Karniadakis
Neural-net-induced Gaussian process regression for function approximation and PDE solution. J. Comput. Phys. 384 (2019)
Fangying Song, George E. Karniadakis
Fractional magneto-hydrodynamics: Algorithms and applications. J. Comput. Phys. 378 (2019)
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)
Liu Yang, George E. Karniadakis
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models. CoRR (2019)
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 (2019)
Yeonjong Shin, George E. Karniadakis
Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks. CoRR (2019)
Ameya D. Jagtap, Kenji Kawaguchi, George E. Karniadakis
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks. CoRR (2019)
Lu Lu, Yeonjong Shin, Yanhui Su, George E. Karniadakis
Dying ReLU and Initialization: Theory and Numerical Examples. CoRR (2019)
Mark S. Alber, Adrian Buganza Tepole, William R. Cannon, Suvranu De, Salvador Dura-Bernal, Krishna C. Garikipati, George E. Karniadakis, William W. Lytton, Paris Perdikaris, Linda R. Petzold, Ellen Kuhl
Integrating machine learning and multiscale modeling - perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. npj Digit. Medicine 2 (2019)
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 (2019)
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) (2019)
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 (2019)
Dongkun Zhang, Ling Guo, George E. Karniadakis
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. CoRR (2019)
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)
Zhen Li, Xin Bian, Yu-Hang Tang, George E. Karniadakis
A dissipative particle dynamics method for arbitrarily complex geometries. J. Comput. Phys. 355 (2018)
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)
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 (2018)
Guofei Pang, Liu Yang, George E. Karniadakis
Neural-net-induced Gaussian process regression for function approximation and PDE solution. CoRR (2018)
Zhijiang Zhang, Weihua Deng, George E. Karniadakis
A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian. SIAM J. Numer. Anal. 56 (5) (2018)
Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou, George E. Karniadakis
Deep Learning of Vortex Induced Vibrations. CoRR (2018)
Dongkun Zhang, Hessam Babaee, George E. Karniadakis
Stochastic Domain Decomposition via Moment Minimization. SIAM J. Sci. Comput. 40 (4) (2018)
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)
Lu Lu, Yanhui Su, George E. Karniadakis
Collapse of Deep and Narrow Neural Nets. CoRR (2018)
Maziar Raissi, George E. Karniadakis
Hidden physics models: Machine learning of nonlinear partial differential equations. J. Comput. Phys. 357 (2018)
Seungjoon Lee, Felix Dietrich, George E. Karniadakis, Ioannis G. Kevrekidis
Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion. CoRR (2018)
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) (2018)
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 (2018)
Maziar Raissi, Alireza Yazdani, George E. Karniadakis
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data. CoRR (2018)
Liu Yang, Dongkun Zhang, George E. Karniadakis
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. CoRR (2018)
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) (2018)
Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Machine Learning of Space-Fractional Differential Equations. CoRR (2018)
Lucia Parussini, Daniele Venturi, Paris Perdikaris, George E. Karniadakis
Multi-fidelity Gaussian process regression for prediction of random fields. J. Comput. Phys. 336 (2017)
Maziar Raissi, George E. Karniadakis
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations. CoRR (2017)
Mingge Deng, Wenxiao Pan, George E. Karniadakis
Anisotropic single-particle dissipative particle dynamics model. J. Comput. Phys. 336 (2017)
Maziar Raissi, George E. Karniadakis
Machine Learning of Linear Differential Equations using Gaussian Processes. CoRR (2017)
Zhiping Mao, George E. Karniadakis
Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods. J. Comput. Phys. 336 (2017)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations. CoRR (2017)
Huan Lei, Xiu Yang, Zhen Li, George E. Karniadakis
Systematic parameter inference in stochastic mesoscopic modeling. J. Comput. Phys. 330 (2017)
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)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. CoRR (2017)
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)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Inferring solutions of differential equations using noisy multi-fidelity data. J. Comput. Phys. 335 (2017)
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 (2017)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Machine learning of linear differential equations using Gaussian processes. J. Comput. Phys. 348 (2017)
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)
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 (2017)
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 (2017)
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) (2017)
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 (2017)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations. CoRR (2017)
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 (2017)
Alireza Yazdani, He Li, Jay D. Humphrey, George E. Karniadakis
A General Shear-Dependent Model for Thrombus Formation. PLoS Comput. Biol. 13 (1) (2017)
Yu-Hang Tang, Dongkun Zhang, George E. Karniadakis
An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields. CoRR (2017)
Fangying Song, Chuanju Xu, George E. Karniadakis
Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations. SIAM J. Sci. Comput. 39 (4) (2017)
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)
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 (2017)
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)
Yue Yu, Paris Perdikaris, George E. Karniadakis
Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. J. Comput. Phys. 323 (2016)
Maziar Raissi, Paris Perdikaris, George E. Karniadakis
Inferring solutions of differential equations using noisy multi-fidelity data. CoRR (2016)
Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis
Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. J. Comput. Phys. 307 (2016)
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)
Maziar Raissi, George E. Karniadakis
Deep Multi-fidelity Gaussian Processes. CoRR (2016)
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)
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)
Heyrim Cho, Daniele Venturi, George E. Karniadakis
Numerical methods for high-dimensional probability density function equations. J. Comput. Phys. 305 (2016)
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 (2016)
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 (2016)
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) (2016)
Zhongqiang Zhang, Fanhai Zeng, George E. Karniadakis
Optimal Error Estimates of Spectral Petrov-Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations. SIAM J. Numer. Anal. 53 (4) (2015)
Mohsen Zayernouri, Mark Ainsworth, George E. Karniadakis
Tempered Fractional Sturm-Liouville EigenProblems. SIAM J. Sci. Comput. 37 (4) (2015)
Xuan Zhao, Zhi-Zhong Sun, George E. Karniadakis
Second-order approximations for variable order fractional derivatives: Algorithms and applications. J. Comput. Phys. 293 (2015)
Diego Rossinelli, Yu-Hang Tang, Kirill Lykov, Dmitry Alexeev, Massimo Bernaschi, Panagiotis E. Hadjidoukas, Mauro Bisson, Wayne Joubert, Christian Conti, George E. Karniadakis, Massimiliano Fatica, Igor Pivkin, Petros Koumoutsakos
The in-silico lab-on-a-chip: petascale and high-throughput simulations of microfluidics at cell resolution. SC (2015)
Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis
Numerical Methods for Stochastic Delay Differential Equations Via the Wong-Zakai Approximation. SIAM J. Sci. Comput. 37 (1) (2015)
Kirill Lykov, Xuejin Li, Huan Lei, Igor V. Pivkin, George E. Karniadakis
Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees. PLoS Comput. Biol. 11 (8) (2015)
Zhen Li, Yu-Hang Tang, Xuejin Li, George E. Karniadakis
Mesoscale modeling of phase transition dynamics of thermoresponsive polymers. CoRR (2015)
Zhongqiang Zhang, Michael V. Tretyakov, Boris Rozovskii, George E. Karniadakis
Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise. SIAM J. Numer. Anal. 53 (1) (2015)
Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis
Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions. SIAM J. Sci. Comput. 37 (4) (2015)
Changho Kim, Oleg Borodin, George E. Karniadakis
Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids. J. Comput. Phys. 302 (2015)
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 (2015)
George E. Karniadakis, Jan S. Hesthaven, Igor Podlubny
Special Issue on "Fractional PDEs: Theory, Numerics, and Applications". J. Comput. Phys. 293 (2015)
Heyrim Cho, Xiu Yang, Daniele Venturi, George E. Karniadakis
Algorithms for Propagating Uncertainty Across Heterogeneous Domains. SIAM J. Sci. Comput. 37 (6) (2015)

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Publication Activity (10 Years)

Top Topics

Top Venues

George E. Karniadakis