George E. Karniadakis

发表

Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions

Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis, 2015, SIAM J. Sci. Comput..

A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains

Suchuan Dong, C. Chryssostomidis, George E. Karniadakis, 2014, J. Comput. Phys..

Deep learning of vortex-induced vibrations pdf

Michael S. Triantafyllou, George E. Karniadakis, Maziar Raissi, 2018, Journal of Fluid Mechanics.

A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative

Zhiping Mao, George E. Karniadakis, G. Karniadakis, 2018, SIAM J. Numer. Anal..

Human arterial tree simulation on TeraGrid

Suchuan Dong, Nicholas T. Karonis, George E. Karniadakis, 2006, SC.

Dual-level parallelism for high-order CFD methods

Suchuan Dong, George E. Karniadakis, G. Karniadakis, 2004, Parallel Comput..

Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise

Zhongqiang Zhang, George E. Karniadakis, Boris Rozovskii, 2015, SIAM J. Numer. Anal..

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations pdf

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2017, ArXiv.

Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion

Seungjoon Lee, George E. Karniadakis, Ioannis G. Kevrekidis, 2018, Interface Focus.

Numerical solution of the Stratonovich- and Ito-Euler equations: Application to the stochastic piston problem

Xiu Yang, Guang Lin, Zhongqiang Zhang, 2013, J. Comput. Phys..

Simulating and visualizing the human arterial system on the TeraGrid

Michael E. Papka, Suchuan Dong, Joseph A. Insley, 2006, Future Gener. Comput. Syst..

Triple-decker: Interfacing atomistic-mesoscopic-continuum flow regimes

George E. Karniadakis, Dmitry A. Fedosov, G. Karniadakis, 2009, J. Comput. Phys..

Unsteady Two-Dimensional Flows in Complex Geometries: Comparative Bifurcation Studies with Global Eigenfunction Expansions

George E. Karniadakis, Paul F. Batcho, Ioannis G. Kevrekidis, 1997, SIAM J. Sci. Comput..

Reweighted ℓ1ℓ1 minimization method for stochastic elliptic differential equations

Xiu Yang, George E. Karniadakis, G. Karniadakis, 2013, J. Comput. Phys..

An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields

George E. Karniadakis, Yu-Hang Tang, Dongkun Zhang, 2018, The Journal of chemical physics.

Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces

George E. Karniadakis, Mingge Deng, Alireza Yazdani, 2016, J. Comput. Phys..

Uncertainty quantification in simulation science

George E. Karniadakis, James Glimm, J. Glimm, 2006, J. Comput. Phys..

Mesoscale modeling of phase transition dynamics of thermoresponsive polymers

Zhen Li, George E. Karniadakis, Xuejin Li, 2015, Chemical communications.

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Guofei Pang, George E. Karniadakis, Michael L. Parks, 2020, J. Comput. Phys..

Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques

Giovanni Marucci, Xiu Yang, Paolo Maffezzoni, 2014, Proceedings of the IEEE 2014 Custom Integrated Circuits Conference.

Electronic poster: visualizing multiscale simulation data

Michael E. Papka, Joseph A. Insley, George E. Karniadakis, 2011, SC '11 Companion.

Grid solutions for biological and physical cross-site simulations on the TeraGrid

Suchuan Dong, Nicholas T. Karonis, George E. Karniadakis, 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows

Dongbin Xiu, Suchuan Dong, Spencer J. Sherwin, 2005, J. Sci. Comput..

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

George E. Karniadakis, Mohsen Zayernouri, G. Karniadakis, 2013, J. Comput. Phys..

Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes

George E. Karniadakis, Didier Lucor, Chau-Hsing Su, 2004, International Conference on Computational Science.

GPU-accelerated red blood cells simulations with transport dissipative particle dynamics

George E. Karniadakis, Zhen Li, Xuejin Li, 2017, Comput. Phys. Commun..

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications pdf

Guofei Pang, George E. Karniadakis, Marta D'Elia, 2020, J. Comput. Phys..

Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids

George E. Karniadakis, Changho Kim, Oleg Borodin, 2015, J. Comput. Phys..

Time Correlation Functions of Brownian Motion and Evaluation of Friction Coefficient in the Near-Brownian-Limit Regime

George E. Karniadakis, Changho Kim, G. Karniadakis, 2014, Multiscale Model. Simul..

A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations

Ian W. Turner, George E. Karniadakis, Kevin Burrage, 2018, SIAM J. Sci. Comput..

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

Daniele Venturi, Paris Perdikaris, George E. Karniadakis, 2016, SIAM J. Sci. Comput..

Generalized fictitious methods for fluid-structure interactions: Analysis and simulations

Yue Yu, George E. Karniadakis, Hyoungsu Baek, 2013, J. Comput. Phys..

Modeling electrokinetic flows by the smoothed profile method

Xian Luo, George E. Karniadakis, Ali Beskok, 2010, J. Comput. Phys..

Multilevel Parallelization Models in CFD

Suchuan Dong, George E. Karniadakis, G. Karniadakis, 2004, J. Aerosp. Comput. Inf. Commun..

Preface

George E. Karniadakis, Grace C. Y. Peng, Ching-Long Lin, 2013, J. Comput. Phys..

Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization

Wei Cai, Paris Perdikaris, Guofei Pang, 2017, J. Comput. Phys..

A General Shear-Dependent Model for Thrombus Formation

He Li, George E. Karniadakis, Jay D. Humphrey, 2017, PLoS Comput. Biol..

Parallel Scientific Computing in C++ and MPI - A Seamless Approach to Parallel Algorithms and their Implementation

Robert Michael Kirby, George E. Karniadakis, G. Karniadakis, 2003 .

Optimal Error Estimates of Spectral Petrov-Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations

Zhongqiang Zhang, George E. Karniadakis, Fanhai Zeng, 2015, SIAM J. Numer. Anal..

Parallel multiscale simulations of a brain aneurysm

George E. Karniadakis, Leopold Grinberg, Dmitry A. Fedosov, 2013, J. Comput. Phys..

Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

Robert Michael Kirby, George E. Karniadakis, G. Karniadakis, 2005, J. Sci. Comput..

Deep Multi-fidelity Gaussian Processes pdf

George E. Karniadakis, Maziar Raissi, G. Karniadakis, 2016, ArXiv.

Multi-element probabilistic collocation method in high dimensions

George E. Karniadakis, Jasmine Foo, G. Karniadakis, 2010, J. Comput. Phys..

A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations

Zhongqiang Zhang, George E. Karniadakis, Fanhai Zeng, 2015, SIAM J. Sci. Comput..

Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations

Zhongqiang Zhang, George E. Karniadakis, Fanhai Zeng, 2016, J. Comput. Phys..

Force-coupling method for flows with ellipsoidal particles

D. Liu, George E. Karniadakis, Martin R. Maxey, 2009, J. Comput. Phys..

Predicting shock dynamics in the presence of uncertainties

Guang Lin, George E. Karniadakis, Chau-Hsing Su, 2006, J. Comput. Phys..

Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations

Daniele Venturi, George E. Karniadakis, Heyrim Cho, 2013, SIAM J. Sci. Comput..

Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions

Minseok Choi, Zhongqiang Zhang, George E. Karniadakis, 2012, SIAM J. Sci. Comput..

Blood Flow at Arterial Branches: Complexities to Resolve for the Angioplasty Suite

David H. Laidlaw, George E. Karniadakis, Peter Richardson, 2006, International Conference on Computational Science.

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications

George E. Karniadakis, Xiaoliang Wan, Jasmine Foo, 2008, J. Comput. Phys..

Adaptive Generalized Polynomial Chaos for Nonlinear Random Oscillators

George E. Karniadakis, Didier Lucor, G. Karniadakis, 2005, SIAM J. Sci. Comput..

The in-silico lab-on-a-chip: petascale and high-throughput simulations of microfluidics at cell resolution

Massimo Bernaschi, Mauro Bisson, Massimiliano Fatica, 2015, SC15: International Conference for High Performance Computing, Networking, Storage and Analysis.

Cross-site computations on the TeraGrid

Suchuan Dong, Nicholas T. Karonis, George E. Karniadakis, 2005, Computing in Science & Engineering.

Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models

Guofei Pang, George E. Karniadakis, Michael L. Parks, 2020, AAAI Spring Symposium: MLPS.

A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half Line

George E. Karniadakis, Anna Lischke, Mohsen Zayernouri, 2017, SIAM J. Sci. Comput..

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu, George E. Karniadakis, D. Xiu, 2002, SIAM J. Sci. Comput..

Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations

George E. Karniadakis, Mohsen Zayernouri, G. Karniadakis, 2014, SIAM J. Sci. Comput..

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Xiu Yang, George E. Karniadakis, Ivan V. Oseledets, 2014, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations

George E. Karniadakis, Mohsen Zayernouri, Ehsan Kharazmi, 2016, SIAM J. Sci. Comput..

Machine Learning of Space-Fractional Differential Equations pdf

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2018, SIAM J. Sci. Comput..

Energy-conserving dissipative particle dynamics with temperature-dependent properties

George E. Karniadakis, Zhen Li, Huan Lei, 2014, Journal of Computational Physics.

Gappy data: To Krig or not to Krig?

George E. Karniadakis, Hasan Gunes, Sirod Sirisup, 2006, J. Comput. Phys..

Fractional magneto-hydrodynamics: Algorithms and applications

George E. Karniadakis, Fangying Song, G. Karniadakis, 2019, J. Comput. Phys..

Dual-Level Parallelism for Deterministic and Stochastic CFD Problems

Suchuan Dong, George E. Karniadakis, 2002, ACM/IEEE SC 2002 Conference (SC'02).

OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution

He Li, Lu Lu, George E. Karniadakis, 2017, Biophysical journal.

MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease

He Li, George E. Karniadakis, Xuejin Li, 2016, PLoS Comput. Biol..

Adaptive Wick-Malliavin Approximation to Nonlinear SPDEs with Discrete Random Variables

George E. Karniadakis, Mengdi Zheng, Boris Rozovsky, 2015, SIAM J. Sci. Comput..

Exponentially accurate spectral and spectral element methods for fractional ODEs

George E. Karniadakis, Mohsen Zayernouri, G. Karniadakis, 2014, J. Comput. Phys..

Tightly Coupled Atomistic-Continuum Simulations of Brain Blood Flow on Petaflop Supercomputers

Michael E. Papka, Joseph A. Insley, George E. Karniadakis, 2012, Computing in Science & Engineering.

Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements

Spencer J. Sherwin, George E. Karniadakis, Leopold Grinberg, 2009, Parallel Comput..

Visualizing multiphysics, fluid-structure interaction phenomena in intracranial aneurysms

Michael E. Papka, Paris Perdikaris, Yue Yu, 2016, Parallel Comput..

Anisotropic single-particle dissipative particle dynamics model

George E. Karniadakis, Mingge Deng, Wenxiao Pan, 2017, J. Comput. Phys..

Direct Numerical Simulation of Turbulence with a PC/Linux Cluster: Fact or Fiction?

Robert Michael Kirby, George E. Karniadakis, Constantinos Evangelinos, 1999, ACM/IEEE SC 1999 Conference (SC'99).

A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities

Zhiping Mao, George E. Karniadakis, Fanhai Zeng, 2017, SIAM J. Sci. Comput..

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

Liu Yang, George E. Karniadakis, Dongkun Zhang, 2018, SIAM J. Sci. Comput..

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

Minseok Choi, Hessam Babaee, George E. Karniadakis, 2017, J. Comput. Phys..

Inferring solutions of differential equations using noisy multi-fidelity data

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2016, J. Comput. Phys..

Adaptive ANOVA decomposition of stochastic incompressible and compressible flows

Xiu Yang, Guang Lin, Minseok Choi, 2012, J. Comput. Phys..

Dying ReLU and Initialization: Theory and Numerical Examples pdf

Lu Lu, George E. Karniadakis, Yeonjong Shin, 2019, Communications in Computational Physics.

A general CFD framework for fault-resilient simulations based on multi-resolution information fusion

Seungjoon Lee, George E. Karniadakis, Ioannis G. Kevrekidis, 2017, J. Comput. Phys..

Blood flow: multi-scale modeling and visualization

Michael E. Papka, Joseph A. Insley, George E. Karniadakis, 2011, SC '11 Companion.

Smoothed profile method for particulate flows: Error analysis and simulations

Xian Luo, George E. Karniadakis, Martin R. Maxey, 2009, J. Comput. Phys..

Numerical Methods for Stochastic Delay Differential Equations Via the Wong-Zakai Approximation

Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis, 2015, SIAM J. Sci. Comput..

Multiscale Modeling of Diseases: Overview

George E. Karniadakis, Ming Dao, G. Karniadakis, 2020, Handbook of Materials Modeling.

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

George E. Karniadakis, Maziar Raissi, Alireza Yazdani, 2018, ArXiv.

A Reconstruction Method for Gappy and Noisy Arterial Flow Data

George E. Karniadakis, Alexander Yakhot, T. Anor, 2007, IEEE Transactions on Medical Imaging.

Stochastic Domain Decomposition via Moment Minimization

Hessam Babaee, George E. Karniadakis, Dongkun Zhang, 2018, SIAM J. Sci. Comput..

Hidden physics models: Machine learning of nonlinear partial differential equations pdf

George E. Karniadakis, Maziar Raissi, G. Karniadakis, 2017, J. Comput. Phys..

Communication Performance Models in Prism : A Spectral Element-Fourier Parallel Navier-Stokes Solver

George E. Karniadakis, Constantinos Evangelinos, G. Karniadakis, 1996, Proceedings of the 1996 ACM/IEEE Conference on Supercomputing.

Runtime Visualization of the Human Arterial Tree

Michael E. Papka, Suchuan Dong, Joseph A. Insley, 2007, IEEE Transactions on Visualization and Computer Graphics.

A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation

George E. Karniadakis, B. Yildirim, G. Karniadakis, 2012, J. Comput. Phys..

Time-dependent generalized polynomial chaos

George E. Karniadakis, Marc I. Gerritsma, Peter E. J. Vos, 2010, J. Comput. Phys..

Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods

Franz S. Hover, Michael S. Triantafyllou, George E. Karniadakis, 2010, Reliab. Eng. Syst. Saf..

Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"

Jan S. Hesthaven, Igor Podlubny, George E. Karniadakis, 2015, J. Comput. Phys..

A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows

George E. Karniadakis, Leopold Grinberg, G. Karniadakis, 2010, J. Comput. Phys..

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

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2017, SIAM J. Sci. Comput..

A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian

Weihua Deng, George E. Karniadakis, Zhijiang Zhang, 2018, SIAM J. Numer. Anal..

Uncertainty-Based Design Methods for Flow-Structure Interactions

George E. Karniadakis, 2007 .

A sharp error estimate for the fast Gauss transform

George E. Karniadakis, Xiaoliang Wan, G. Karniadakis, 2006, J. Comput. Phys..

Patient-specific modeling of individual sickle cell behavior under transient hypoxia

Subra Suresh, George E. Karniadakis, Xuejin Li, 2017, PLoS Comput. Biol..

Towards stable coupling methods for high-order discretization of fluid-structure interaction: Algorithms and observations

Robert Michael Kirby, George E. Karniadakis, Zohar Yosibash, 2007, J. Comput. Phys..

A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion

Seungjoon Lee, George E. Karniadakis, Ioannis G. Kevrekidis, 2017, J. Comput. Phys..

Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions

Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis, 2016, SIAM J. Sci. Comput..

Performance Evaluation of Generalized Polynomial Chaos

Dongbin Xiu, George E. Karniadakis, Didier Lucor, 2003, International Conference on Computational Science.

Algorithms for Propagating Uncertainty Across Heterogeneous Domains

Daniele Venturi, Xiu Yang, George E. Karniadakis, 2015, SIAM J. Sci. Comput..

NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications

Shantenu Jha, Suchuan Dong, Peter V. Coveney, 2006, 2006 IEEE Challenges of Large Applications in Distributed Environments.

A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping

George E. Karniadakis, Hyoungsu Baek, G. Karniadakis, 2012, J. Comput. Phys..

Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise

Zhongqiang Zhang, George E. Karniadakis, Boris Rozovskii, 2016, Numerische Mathematik.

NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications

Shantenu Jha, Suchuan Dong, Peter V. Coveney, 2006, CLADE.

Immersive virtual reality for visualizing flow through an artery

Robert Michael Kirby, David H. Laidlaw, George E. Karniadakis, 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes

Wei Cai, Wen Chen, George E. Karniadakis, 2017, Comput. Math. Appl..

Visualization of Vortices in Simulated Airflow around Bat Wings During Flight

David H. Laidlaw, George E. Karniadakis, Sharon Swartz, 2004, IEEE Visualization 2004.

A seamless approach to multiscale complex fluid simulation

George E. Karniadakis, Bruce Caswell, Vasileios Symeonidis, 2005, Computing in Science & Engineering.

Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations

George E. Karniadakis, Fangying Song, Chuanju Xu, 2017, SIAM J. Sci. Comput..

Coarse-Grained Modeling of Protein Unfolding Dynamics

George E. Karniadakis, Mingge Deng, G. Karniadakis, 2014, Multiscale Model. Simul..

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

Paris Perdikaris, Yue Yu, George E. Karniadakis, 2016, J. Comput. Phys..

A Multistage Wiener Chaos Expansion Method for Stochastic Advection-Diffusion-Reaction Equations

Zhongqiang Zhang, George E. Karniadakis, Boris Rozovskii, 2012, SIAM J. Sci. Comput..

Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria

Subra Suresh, George E. Karniadakis, Huan Lei, 2011, PLoS Comput. Biol..

Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

George E. Karniadakis, Xiaoliang Wan, G. Karniadakis, 2006, J. Sci. Comput..

Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation

Dongbin Xiu, George E. Karniadakis, Xiaoliang Wan, 2005, SIAM J. Sci. Comput..

Collapse of Deep and Narrow Neural Nets pdf

Lu Lu, George E. Karniadakis, Yanhui Su, 2018, ArXiv.

A deep convolutional neural network for classification of red blood cells in sickle cell anemia

Hong Zhao, George E. Karniadakis, Mengjia Xu, 2017, PLoS Comput. Biol..

A new computational paradigm in multiscale simulations: Application to brain blood flow

Michael E. Papka, Joseph A. Insley, George E. Karniadakis, 2011, 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

Elsevier Editorial System(tm) for Journal of Computational Physics Manuscript Draft Title: New Evolution Equations for the Joint Response-excitation Probability Density Function of Stochastic Solutions to First-order Nonlinear Pdes New Evolution Equations for the Joint Response-excitation Probabilit

Daniele Venturi, George E. Karniadakis, G. Karniadakis, 2022 .

Numerical studies of the stochastic Korteweg-de Vries equation

Guang Lin, George E. Karniadakis, Leopold Grinberg, 2006, J. Comput. Phys..

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations pdf

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2017, ArXiv.

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

Minseok Choi, George E. Karniadakis, Themistoklis P. Sapsis, 2014, J. Comput. Phys..

Systematic parameter inference in stochastic mesoscopic modeling

Xiu Yang, George E. Karniadakis, Zhen Li, 2016, J. Comput. Phys..

Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations

George E. Karniadakis, Hyoungsu Baek, G. Karniadakis, 2011, J. Comput. Phys..

P-Refinement and P-Threads (Preprint)

George E. Karniadakis, Steven Dong, 2002 .

Multi-fidelity Gaussian process regression for prediction of random fields

Daniele Venturi, Paris Perdikaris, George E. Karniadakis, 2017, J. Comput. Phys..

Basis Functions for Triangular and Quadrilateral High-Order Elements

Timothy C. Warburton, Spencer J. Sherwin, George E. Karniadakis, 1999, SIAM J. Sci. Comput..

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

Xuan Zhao, Zhi-Zhong Sun, George E. Karniadakis, 2015, J. Comput. Phys..

High-Order Algorithms for 3D Plasma Simulations on Unstructured and Hybrid Meshes

George E. Karniadakis, 1999 .

Fractional Spectral Collocation Method

George E. Karniadakis, Mohsen Zayernouri, G. Karniadakis, 2014, SIAM J. Sci. Comput..

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

George E. Karniadakis, Huan Lei, Dmitry A. Fedosov, 2011, J. Comput. Phys..

Stochastic Computational Fluid Mechanics

Guang Lin, George E. Karniadakis, Xiaoliang Wan, 2007, Computing in Science & Engineering.

Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors

Liu Yang, George E. Karniadakis, Dongkun Zhang, 2018, J. Comput. Phys..

Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

Zhiping Mao, George E. Karniadakis, G. Karniadakis, 2017, J. Comput. Phys..

Structural Integrity of a Fighter Aircraft Undergoing Dynamic Combat Maneuvers

George E. Karniadakis, 2004 .

Fractional spectral collocation methods for linear and nonlinear variable order FPDEs

George E. Karniadakis, Mohsen Zayernouri, G. Karniadakis, 2015, J. Comput. Phys..

Parallel Cfd Benchmarks on Cray Computers

George E. Karniadakis, Constantinos Evangelinos, G. Karniadakis, 1996, Parallel Algorithms Appl..

Exact PDF equations and closure approximations for advective-reactive transport

Daniel M. Tartakovsky, Daniele Venturi, Alexandre M. Tartakovsky, 2013, J. Comput. Phys..

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Paris Perdikaris, George E. Karniadakis, Maziar Raissi, 2019, J. Comput. Phys..

Numerical Methods for SPDEs with Tempered Stable Processes

George E. Karniadakis, Mengdi Zheng, G. Karniadakis, 2015, SIAM J. Sci. Comput..

Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees

George E. Karniadakis, Xuejin Li, Huan Lei, 2015, PLoS Comput. Biol..

A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise

Zhongqiang Zhang, George E. Karniadakis, Boris Rozovskii, 2013, SIAM J. Sci. Comput..

Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation

George E. Karniadakis, Chau-Hsing Su, M. Jardak, 2002, J. Sci. Comput..

Simulation and visualization of flow around bat wings during flight

David H. Laidlaw, Rachel Weinstein, George E. Karniadakis, 2004, SIGGRAPH '04.

Visualization of blood platelets in a virtual environment

David H. Laidlaw, George E. Karniadakis, Peter Richardson, 2004, SIGGRAPH '04.

A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints

Wei Cai, George E. Karniadakis, Min Hyung Cho, 2018, SIAM J. Sci. Comput..

Numerical methods for high-dimensional probability density function equations

Daniele Venturi, George E. Karniadakis, Heyrim Cho, 2016, J. Comput. Phys..

A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications

George E. Karniadakis, Vasileios Symeonidis, G. Karniadakis, 2006, J. Comput. Phys..

Velocity limit in DPD simulations of wall-bounded flows

George E. Karniadakis, Dmitry A. Fedosov, Igor Pivkin, 2008, J. Comput. Phys..

DeepXDE: A Deep Learning Library for Solving Differential Equations pdf

Zhiping Mao, Lu Lu, George E. Karniadakis, 2019, AAAI Spring Symposium: MLPS.

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers pdf

Zhen Li, George E. Karniadakis, Shuhei Kudo, 2014, J. Comput. Phys..

Simulation and Visualization of Air Flow Around Bat Wings During Flight

David H. Laidlaw, Rachel Weinstein, George E. Karniadakis, 2005, International Conference on Computational Science.

Neural-net-induced Gaussian process regression for function approximation and PDE solution pdf

Liu Yang, Guofei Pang, George E. Karniadakis, 2018, J. Comput. Phys..

A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes

Minseok Choi, George E. Karniadakis, Themistoklis P. Sapsis, 2013, J. Comput. Phys..

Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows

Jie Ouyang, Lifei Zhao, George E. Karniadakis, 2017, J. Comput. Phys..

Accelerating dissipative particle dynamics simulations on GPUs: Algorithms, numerics and applications pdf

George E. Karniadakis, Yu-Hang Tang, G. Karniadakis, 2013, Comput. Phys. Commun..

A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

Jin Xu, Dongbin Xiu, George E. Karniadakis, 2002, J. Sci. Comput..

Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition

George E. Karniadakis, Zhen Li, Xin Bian, 2015, J. Comput. Phys..

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

George E. Karniadakis, Tamer A. Zaki, Olaf Marxen, 2020, J. Comput. Phys..

Biomechanics of red blood cells in human spleen and consequences for physiology and disease

Subra Suresh, George E. Karniadakis, Igor V. Pivkin, 2016, Proceedings of the National Academy of Sciences.

Predicting human blood viscosity in silico

Gerhard Gompper, George E. Karniadakis, Dmitry A. Fedosov, 2011, Proceedings of the National Academy of Sciences.

Lipid bilayer and cytoskeletal interactions in a red blood cell

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