George E. Karniadakis

212 papers A 9Misc 4Journal 188Unranked 10

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Deep Neural networks for solving high-dimensional parabolic partial differential equations. CoRR Wenzhong Zhang, Zheyuan Hu, Wei Cai, George E. Karniadakis
2025	J	`jnl`	AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning. CoRR Qile Jiang, George E. Karniadakis
2025	J	`jnl`	Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs. SIAM J. Sci. Comput. Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George E. Karniadakis, Kenji Kawaguchi
2025	J	`jnl`	Equilibrium Conserving Neural Operators for Super-Resolution Learning. CoRR Vivek Oommen, Andreas E. Robertson, Daniel Diaz, Coleman Alleman, Zhen Zhang, Anthony D. Rollett, George E. Karniadakis, Rémi Dingreville
2025	J	`jnl`	Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators. CoRR David S. Li, Somdatta Goswami, Qianying Cao, Vivek Oommen, Roland Assi, Jay D. Humphrey, George E. Karniadakis
2025	J	`jnl`	Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators. PLoS Comput. Biol. David S. Li, Somdatta Goswami, Qianying Cao, Vivek Oommen, Roland Assi, Jay D. Humphrey, George E. Karniadakis
2025	J	`jnl`	Physics-Informed Computer Vision: A Review and Perspectives. ACM Comput. Surv. Chayan Banerjee, Kien Nguyen, Clinton Fookes, George E. Karniadakis
2025	J	`jnl`	Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates. CoRR Aniruddha Bora, Shixuan Zhang, Khemraj Shukla, Bryce E. Harrop, George E. Karniadakis, L. Ruby Leung
2025	J	`jnl`	Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations. SIAM J. Sci. Comput. Zheyuan Hu, Zhongqiang Zhang, George E. Karniadakis, Kenji Kawaguchi
2025	—	`conf`	Towards Non-invasive Estimation of Myocardial Scar Stiffness from Cardiac Strains Using Deep Learning. FIMH (1) Rana Raza Mehdi, Nikhil Kadivar, Vahid Serpooshan, Kyle J. Myers, George E. Karniadakis, Reza Avazmohammadi
2025	J	`jnl`	XAI4Extremes: An interpretable machine learning framework for understanding extreme-weather precursors under climate change. CoRR Jiawen Wei, Aniruddha Bora, Vivek Oommen, Chenyu Dong, Juntao Yang, Jeff Adie, Chen Chen, Simon See, George E. Karniadakis, Gianmarco Mengaldo
2024	J	`jnl`	Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning. CoRR Minglei Lu, Chensen Lin, Martian Maxey, George E. Karniadakis, Zhen Li
2024	J	`jnl`	Enhancing Training of Physics-Informed Neural Networks Using Domain Decomposition-Based Preconditioning Strategies. SIAM J. Sci. Comput. Alena Kopanicáková, Hardik Kothari, George E. Karniadakis, Rolf Krause
2024	J	`jnl`	NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators. SIAM Rev. Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George E. Karniadakis
2023	J	`jnl`	High-order methods for hypersonic flows with strong shocks and real chemistry. J. Comput. Phys. Ahmad Peyvan, Khemraj Shukla, Jesse Chan, George E. Karniadakis
2022	J	`jnl`	Computational investigation of blood cell transport in retinal microaneurysms. PLoS Comput. Biol. He Li, Yixiang Deng, Konstantina Sampani, Shengze Cai, Zhen Li, Jennifer K. Sun, George E. Karniadakis
2022	J	`jnl`	Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models. SIAM J. Sci. Comput. Liu Yang, Constantinos Daskalakis, George E. Karniadakis
2022	J	`jnl`	Multifidelity Deep Operator Networks. CoRR Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis
2022	J	`jnl`	Multiphysics and multiscale modeling of microthrombosis in COVID-19. PLoS Comput. Biol. He Li, Yixiang Deng, Zhen Li, Ander Dorken Gallastegi, Christos S. Mantzoros, Galit H. Frydman, George E. Karniadakis
2022	J	`jnl`	SympOCnet: Solving Optimal Control Problems with Applications to High-Dimensional Multiagent Path Planning Problems. SIAM J. Sci. Comput. Tingwei Meng, Zhen Zhang, Jérôme Darbon, George E. Karniadakis
2021	J	`jnl`	A physics-informed variational DeepONet for predicting the crack path in brittle materials. CoRR Somdatta Goswami, Minglang Yin, Yue Yu, George E. Karniadakis
2021	J	`jnl`	An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City. PLoS Comput. Biol. Sheng Zhang, Joan Ponce, Zhen Zhang, Guang Lin, George E. Karniadakis
2021	—	`conf`	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 Ameya D. Jagtap, George E. Karniadakis
2020	J	`jnl`	A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels. PLoS Comput. Biol. Xiaoning Zheng, Alireza Yazdani, He Li, Jay D. Humphrey, George E. Karniadakis
2020	—	`conf`	Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models. AAAI Spring Symposium: MLPS Marta D'Elia, George E. Karniadakis, Guofei Pang, Michael L. Parks
2020	J	`jnl`	nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. J. Comput. Phys. Guofei Pang, Marta D'Elia, Michael L. Parks, George E. Karniadakis
2020	J	`jnl`	nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications. CoRR Guofei Pang, Marta D'Elia, Michael L. Parks, George E. Karniadakis
2019	J	`jnl`	A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions. SIAM J. Sci. Comput. Nan Wang, Zhiping Mao, Chengming Huang, George E. Karniadakis
2019	J	`jnl`	A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics. Sci. Robotics Dixia Fan, Gurvan Jodin, Thomas Consi, L. Bonfiglio, Y. Ma, Elizabeth Keyes, George E. Karniadakis, Michael S. Triantafyllou
2019	J	`jnl`	DeepXDE: A deep learning library for solving differential equations. CoRR Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis
2019	J	`jnl`	Dying ReLU and Initialization: Theory and Numerical Examples. CoRR Lu Lu, Yeonjong Shin, Yanhui Su, George E. Karniadakis
2019	J	`jnl`	Fractional magneto-hydrodynamics: Algorithms and applications. J. Comput. Phys. Fangying Song, George E. Karniadakis
2019	—	`conf`	Highly-Ccalable, Physics-Informed GANs for Learning Solutions of Stochastic PDEs. DLS@SC 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
2019	J	`jnl`	Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs. CoRR 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
2019	J	`jnl`	Integrating machine learning and multiscale modeling - perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. npj Digit. Medicine 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
2019	J	`jnl`	Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. CoRR Dongkun Zhang, Ling Guo, George E. Karniadakis
2019	J	`jnl`	Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks. CoRR Ameya D. Jagtap, Kenji Kawaguchi, George E. Karniadakis
2019	J	`jnl`	Machine Learning of Space-Fractional Differential Equations. SIAM J. Sci. Comput. Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2019	J	`jnl`	Neural-net-induced Gaussian process regression for function approximation and PDE solution. J. Comput. Phys. Guofei Pang, Liu Yang, George E. Karniadakis
2019	J	`jnl`	Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2019	J	`jnl`	Physics-informed semantic inpainting: Application to geostatistical modeling. CoRR Qiang Zheng, Lingzao Zeng, George E. Karniadakis
2019	J	`jnl`	Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models. CoRR Liu Yang, George E. Karniadakis
2019	J	`jnl`	Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. CoRR Pengzhan Jin, Lu Lu, Yifa Tang, George E. Karniadakis
2019	J	`jnl`	Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics. J. Comput. Phys. Ansel L. Blumers, Zhen Li, George E. Karniadakis
2019	J	`jnl`	Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks. CoRR Yeonjong Shin, George E. Karniadakis
2018	J	`jnl`	A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints. SIAM J. Sci. Comput. Ivi C. Tsantili, Min Hyung Cho, Wei Cai, George E. Karniadakis
2018	J	`jnl`	A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations. SIAM J. Sci. Comput. Fanhai Zeng, Ian W. Turner, Kevin Burrage, George E. Karniadakis
2018	J	`jnl`	A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian. SIAM J. Numer. Anal. Zhijiang Zhang, Weihua Deng, George E. Karniadakis
2018	J	`jnl`	A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative. SIAM J. Numer. Anal. Zhiping Mao, George E. Karniadakis
2018	J	`jnl`	A dissipative particle dynamics method for arbitrarily complex geometries. J. Comput. Phys. Zhen Li, Xin Bian, Yu-Hang Tang, George E. Karniadakis
2018	J	`jnl`	Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. J. Comput. Phys. Lifei Zhao, Zhen Li, Bruce Caswell, Jie Ouyang, George E. Karniadakis
2018	J	`jnl`	Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors. J. Comput. Phys. Dongkun Zhang, Liu Yang, George E. Karniadakis
2018	J	`jnl`	Collapse of Deep and Narrow Neural Nets. CoRR Lu Lu, Yanhui Su, George E. Karniadakis
2018	J	`jnl`	Deep Learning of Vortex Induced Vibrations. CoRR Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou, George E. Karniadakis
2018	J	`jnl`	Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data. CoRR Maziar Raissi, Alireza Yazdani, George E. Karniadakis
2018	J	`jnl`	Hidden physics models: Machine learning of nonlinear partial differential equations. J. Comput. Phys. Maziar Raissi, George E. Karniadakis
2018	J	`jnl`	Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion. CoRR Seungjoon Lee, Felix Dietrich, George E. Karniadakis, Ioannis G. Kevrekidis
2018	J	`jnl`	Machine Learning of Space-Fractional Differential Equations. CoRR Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2018	J	`jnl`	Neural-net-induced Gaussian process regression for function approximation and PDE solution. CoRR Guofei Pang, Liu Yang, George E. Karniadakis
2018	J	`jnl`	Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations. SIAM J. Sci. Comput. Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2018	J	`jnl`	Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. CoRR Liu Yang, Dongkun Zhang, George E. Karniadakis
2018	J	`jnl`	Stochastic Domain Decomposition via Moment Minimization. SIAM J. Sci. Comput. Dongkun Zhang, Hessam Babaee, George E. Karniadakis
2017	J	`jnl`	A General Shear-Dependent Model for Thrombus Formation. PLoS Comput. Biol. Alireza Yazdani, He Li, Jay D. Humphrey, George E. Karniadakis
2017	J	`jnl`	A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities. SIAM J. Sci. Comput. Fanhai Zeng, Zhiping Mao, George E. Karniadakis
2017	J	`jnl`	A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half Line. SIAM J. Sci. Comput. Anna Lischke, Mohsen Zayernouri, George E. Karniadakis
2017	J	`jnl`	A deep convolutional neural network for classification of red blood cells in sickle cell anemia. PLoS Comput. Biol. Mengjia Xu, Dimitrios P. Papageorgiou, Sabia Z. Abidi, Ming Dao, Hong Zhao, George E. Karniadakis
2017	J	`jnl`	A general CFD framework for fault-resilient simulations based on multi-resolution information fusion. J. Comput. Phys. Seungjoon Lee, Ioannis G. Kevrekidis, George E. Karniadakis
2017	J	`jnl`	A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion. J. Comput. Phys. Seungjoon Lee, Ioannis G. Kevrekidis, George E. Karniadakis
2017	J	`jnl`	A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems. J. Comput. Phys. Hessam Babaee, Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis
2017	J	`jnl`	An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields. CoRR Yu-Hang Tang, Dongkun Zhang, George E. Karniadakis
2017	J	`jnl`	Anisotropic single-particle dissipative particle dynamics model. J. Comput. Phys. Mingge Deng, Wenxiao Pan, George E. Karniadakis
2017	J	`jnl`	Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations. SIAM J. Sci. Comput. Fangying Song, Chuanju Xu, George E. Karniadakis
2017	J	`jnl`	Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. J. Comput. Phys. Guofei Pang, Paris Perdikaris, Wei Cai, George E. Karniadakis
2017	J	`jnl`	Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes. Comput. Math. Appl. Fangying Song, Fanhai Zeng, Wei Cai, Wen Chen, George E. Karniadakis
2017	J	`jnl`	Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods. J. Comput. Phys. Zhiping Mao, George E. Karniadakis
2017	J	`jnl`	GPU-accelerated red blood cells simulations with transport dissipative particle dynamics. Comput. Phys. Commun. Ansel L. Blumers, Yu-Hang Tang, Zhen Li, Xuejin Li, George E. Karniadakis
2017	J	`jnl`	Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations. CoRR Maziar Raissi, George E. Karniadakis
2017	J	`jnl`	Inferring solutions of differential equations using noisy multi-fidelity data. J. Comput. Phys. Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	Machine Learning of Linear Differential Equations using Gaussian Processes. CoRR Maziar Raissi, George E. Karniadakis
2017	J	`jnl`	Machine learning of linear differential equations using Gaussian processes. J. Comput. Phys. Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	Multi-fidelity Gaussian process regression for prediction of random fields. J. Comput. Phys. Lucia Parussini, Daniele Venturi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations. CoRR Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution. CoRR Yu-Hang Tang, Lu Lu, He Li, Constantinos Evangelinos, Leopold Grinberg, Vipin Sachdeva, George E. Karniadakis
2017	J	`jnl`	Patient-specific modeling of individual sickle cell behavior under transient hypoxia. PLoS Comput. Biol. Xuejin Li, E. Du, Ming Dao, Subra Suresh, George E. Karniadakis
2017	J	`jnl`	Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations. SIAM J. Sci. Comput. Ehsan Kharazmi, Mohsen Zayernouri, George E. Karniadakis
2017	J	`jnl`	Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. CoRR Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations. CoRR Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2017	J	`jnl`	Systematic parameter inference in stochastic mesoscopic modeling. J. Comput. Phys. Huan Lei, Xiu Yang, Zhen Li, George E. Karniadakis
2016	J	`jnl`	Deep Multi-fidelity Gaussian Processes. CoRR Maziar Raissi, George E. Karniadakis
2016	J	`jnl`	Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations. J. Comput. Phys. Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis
2016	J	`jnl`	Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces. J. Comput. Phys. Alireza Yazdani, Mingge Deng, Bruce Caswell, George E. Karniadakis
2016	J	`jnl`	Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. J. Comput. Phys. Yue Yu, Paris Perdikaris, George E. Karniadakis
2016	J	`jnl`	Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions. SIAM J. Sci. Comput. Wanrong Cao, Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis
2016	J	`jnl`	Inferring solutions of differential equations using noisy multi-fidelity data. CoRR Maziar Raissi, Paris Perdikaris, George E. Karniadakis
2016	J	`jnl`	MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease. PLoS Comput. Biol. Hung-Yu Chang, Xuejin Li, He Li, George E. Karniadakis
2016	J	`jnl`	Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets. SIAM J. Sci. Comput. Paris Perdikaris, Daniele Venturi, George E. Karniadakis
2016	J	`jnl`	Numerical methods for high-dimensional probability density function equations. J. Comput. Phys. Heyrim Cho, Daniele Venturi, George E. Karniadakis
2016	J	`jnl`	Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise. Numerische Mathematik Zhongqiang Zhang, Boris Rozovskii, George E. Karniadakis
2016	J	`jnl`	Visualizing multiphysics, fluid-structure interaction phenomena in intracranial aneurysms. Parallel Comput. Paris Perdikaris, Joseph A. Insley, Leopold Grinberg, Yue Yu, Michael E. Papka, George E. Karniadakis
2015	J	`jnl`	A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations. SIAM J. Sci. Comput. Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis
2015	J	`jnl`	Adaptive Wick-Malliavin Approximation to Nonlinear SPDEs with Discrete Random Variables. SIAM J. Sci. Comput. Mengdi Zheng, Boris L. Rozovsky, George E. Karniadakis
2015	J	`jnl`	Algorithms for Propagating Uncertainty Across Heterogeneous Domains. SIAM J. Sci. Comput. Heyrim Cho, Xiu Yang, Daniele Venturi, George E. Karniadakis
2015	J	`jnl`	Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. Zheng Zhang, Xiu Yang, Ivan V. Oseledets, George E. Karniadakis, Luca Daniel
2015	J	`jnl`	Fractional spectral collocation methods for linear and nonlinear variable order FPDEs. J. Comput. Phys. Mohsen Zayernouri, George E. Karniadakis
2015	J	`jnl`	Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees. PLoS Comput. Biol. Kirill Lykov, Xuejin Li, Huan Lei, Igor V. Pivkin, George E. Karniadakis
2015	J	`jnl`	Mesoscale modeling of phase transition dynamics of thermoresponsive polymers. CoRR Zhen Li, Yu-Hang Tang, Xuejin Li, George E. Karniadakis
2015	J	`jnl`	Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition. J. Comput. Phys. Xin Bian, Zhen Li, George E. Karniadakis
2015	J	`jnl`	Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers. J. Comput. Phys. Yu-Hang Tang, Shuhei Kudo, Xin Bian, Zhen Li, George E. Karniadakis
2015	J	`jnl`	Numerical Methods for SPDEs with Tempered Stable Processes. SIAM J. Sci. Comput. Mengdi Zheng, George E. Karniadakis
2015	J	`jnl`	Numerical Methods for Stochastic Delay Differential Equations Via the Wong-Zakai Approximation. SIAM J. Sci. Comput. Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis
2015	J	`jnl`	Optimal Error Estimates of Spectral Petrov-Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations. SIAM J. Numer. Anal. Zhongqiang Zhang, Fanhai Zeng, George E. Karniadakis
2015	J	`jnl`	Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids. J. Comput. Phys. Changho Kim, Oleg Borodin, George E. Karniadakis
2015	J	`jnl`	Second-order approximations for variable order fractional derivatives: Algorithms and applications. J. Comput. Phys. Xuan Zhao, Zhi-Zhong Sun, George E. Karniadakis
2015	J	`jnl`	Special Issue on "Fractional PDEs: Theory, Numerics, and Applications". J. Comput. Phys. George E. Karniadakis, Jan S. Hesthaven, Igor Podlubny
2015	J	`jnl`	Tempered Fractional Sturm-Liouville EigenProblems. SIAM J. Sci. Comput. Mohsen Zayernouri, Mark Ainsworth, George E. Karniadakis
2015	A	`conf`	The in-silico lab-on-a-chip: petascale and high-throughput simulations of microfluidics at cell resolution. SC 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
2015	J	`jnl`	Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions. SIAM J. Sci. Comput. Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis
2015	J	`jnl`	Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise. SIAM J. Numer. Anal. Zhongqiang Zhang, Michael V. Tretyakov, Boris Rozovskii, George E. Karniadakis
2014	J	`jnl`	A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise. SIAM J. Sci. Comput. Zhongqiang Zhang, Michael V. Tretyakov, Boris Rozovskii, George E. Karniadakis
2014	J	`jnl`	A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. Suchuan Dong, George E. Karniadakis, Chryssostomos Chryssostomidis
2014	J	`jnl`	Accelerating dissipative particle dynamics simulations on GPUs: Algorithms, numerics and applications. Comput. Phys. Commun. Yu-Hang Tang, George E. Karniadakis
2014	J	`jnl`	Coarse-Grained Modeling of Protein Unfolding Dynamics. Multiscale Model. Simul. Mingge Deng, George E. Karniadakis
2014	J	`jnl`	Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations. SIAM J. Sci. Comput. Mohsen Zayernouri, George E. Karniadakis
2014	J	`jnl`	Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition. CoRR Zheng Zhang, Xiu Yang, Ivan V. Oseledets, George E. Karniadakis, Luca Daniel
2014	J	`jnl`	Energy-conserving dissipative particle dynamics with temperature-dependent properties. J. Comput. Phys. Zhen Li, Yu-Hang Tang, Huan Lei, Bruce Caswell, George E. Karniadakis
2014	J	`jnl`	Exponentially accurate spectral and spectral element methods for fractional ODEs. J. Comput. Phys. Mohsen Zayernouri, George E. Karniadakis
2014	J	`jnl`	Fractional Spectral Collocation Method. SIAM J. Sci. Comput. Mohsen Zayernouri, George E. Karniadakis
2014	J	`jnl`	Multiscale Universal Interface: A Concurrent Framework for Coupling Heterogeneous Solvers. CoRR Yu-Hang Tang, Shuhei Kudo, Xin Bian, Zhen Li, George E. Karniadakis
2014	J	`jnl`	On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations. J. Comput. Phys. Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis
2014	J	`jnl`	Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations. SIAM J. Sci. Comput. Mohsen Zayernouri, Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis
2014	J	`jnl`	Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques. CoRR Zheng Zhang, Xiu Yang, Giovanni Marucci, Paolo Maffezzoni, Ibrahim M. Elfadel, George E. Karniadakis, Luca Daniel
2014	—	`conf`	Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques. CICC Zheng Zhang, Xiu Yang, Giovanni Marucci, Paolo Maffezzoni, Ibrahim Abe M. Elfadel, George E. Karniadakis, Luca Daniel
2014	J	`jnl`	Time Correlation Functions of Brownian Motion and Evaluation of Friction Coefficient in the Near-Brownian-Limit Regime. Multiscale Model. Simul. Changho Kim, George E. Karniadakis
2013	J	`jnl`	A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes. J. Comput. Phys. Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis
2013	J	`jnl`	Accelerating Dissipative Particle Dynamics Simulations on GPUs: Algorithms, Numerics and Applications. CoRR Yu-Hang Tang, George E. Karniadakis
2013	J	`jnl`	Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations. SIAM J. Sci. Comput. Heyrim Cho, Daniele Venturi, George E. Karniadakis
2013	J	`jnl`	Exact PDF equations and closure approximations for advective-reactive transport. J. Comput. Phys. Daniele Venturi, Daniel M. Tartakovsky, Alexandre M. Tartakovsky, George E. Karniadakis
2013	J	`jnl`	Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation. J. Comput. Phys. Mohsen Zayernouri, George E. Karniadakis
2013	J	`jnl`	Generalized fictitious methods for fluid-structure interactions: Analysis and simulations. J. Comput. Phys. Yue Yu, Hyoungsu Baek, George E. Karniadakis
2013	J	`jnl`	Numerical solution of the Stratonovich- and Ito-Euler equations: Application to the stochastic piston problem. J. Comput. Phys. Zhongqiang Zhang, Xiu Yang, Guang Lin, George E. Karniadakis
2013	J	`jnl`	Parallel multiscale simulations of a brain aneurysm. J. Comput. Phys. Leopold Grinberg, Dmitry A. Fedosov, George E. Karniadakis
2013	J	`jnl`	Preface. J. Comput. Phys. Ching-Long Lin, Grace C. Y. Peng, George E. Karniadakis
2013	J	`jnl`	Reweighted J. Comput. Phys. Xiu Yang, George E. Karniadakis
2012	J	`jnl`	A Multistage Wiener Chaos Expansion Method for Stochastic Advection-Diffusion-Reaction Equations. SIAM J. Sci. Comput. Zhongqiang Zhang, Boris Rozovskii, Michael V. Tretyakov, George E. Karniadakis
2012	J	`jnl`	A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. J. Comput. Phys. Hyoungsu Baek, George E. Karniadakis
2012	J	`jnl`	A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation. J. Comput. Phys. B. Yildirim, George E. Karniadakis
2012	J	`jnl`	Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. J. Comput. Phys. Xiu Yang, Minseok Choi, Guang Lin, George E. Karniadakis
2012	J	`jnl`	Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions. SIAM J. Sci. Comput. Zhongqiang Zhang, Minseok Choi, George E. Karniadakis
2012	J	`jnl`	New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs. J. Comput. Phys. Daniele Venturi, George E. Karniadakis
2012	J	`jnl`	Tightly Coupled Atomistic-Continuum Simulations of Brain Blood Flow on Petaflop Supercomputers. Comput. Sci. Eng. Leopold Grinberg, Joseph A. Insley, Dmitry A. Fedosov, Vitali A. Morozov, Michael E. Papka, George E. Karniadakis
2011	A	`conf`	A new computational paradigm in multiscale simulations: application to brain blood flow. SC Leopold Grinberg, Joseph A. Insley, Vitali A. Morozov, Michael E. Papka, George E. Karniadakis, Dmitry A. Fedosov, Kalyan Kumaran
2011	—	`conf`	Blood flow: multi-scale modeling and visualization. SC Companion Joseph A. Insley, Leopold Grinberg, Dmitry A. Fedosov, Vitali A. Morozov, Bruce Caswell, Michael E. Papka, George E. Karniadakis
2011	—	`conf`	Electronic poster: visualizing multiscale simulation data. SC Companion Joseph A. Insley, Leopold Grinberg, Michael E. Papka, George E. Karniadakis
2011	J	`jnl`	Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria. PLoS Comput. Biol. Dmitry A. Fedosov, Huan Lei, Bruce Caswell, Subra Suresh, George E. Karniadakis
2011	J	`jnl`	Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations. J. Comput. Phys. Hyoungsu Baek, George E. Karniadakis
2011	J	`jnl`	Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics. J. Comput. Phys. Huan Lei, Dmitry A. Fedosov, George E. Karniadakis
2010	J	`jnl`	A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows. J. Comput. Phys. Leopold Grinberg, George E. Karniadakis
2010	J	`jnl`	Modeling electrokinetic flows by the smoothed profile method. J. Comput. Phys. Xian Luo, Ali Beskok, George E. Karniadakis
2010	J	`jnl`	Multi-element probabilistic collocation method in high dimensions. J. Comput. Phys. Jasmine Foo, George E. Karniadakis
2010	J	`jnl`	Time-dependent generalized polynomial chaos. J. Comput. Phys. Marc I. Gerritsma, Jan-Bart van der Steen, Peter Vos, George E. Karniadakis
2010	J	`jnl`	Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods. Reliab. Eng. Syst. Saf. Pradya Prempraneerach, Franz S. Hover, Michael S. Triantafyllou, George E. Karniadakis
2009	J	`jnl`	Force-coupling method for flows with ellipsoidal particles. J. Comput. Phys. D. Liu, Eric E. Keaveny, Martin R. Maxey, George E. Karniadakis
2009	J	`jnl`	Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements. Parallel Comput. Leopold Grinberg, Dmitry Pekurovsky, Spencer J. Sherwin, George E. Karniadakis
2009	J	`jnl`	Smoothed profile method for particulate flows: Error analysis and simulations. J. Comput. Phys. Xian Luo, Martin R. Maxey, George E. Karniadakis
2009	J	`jnl`	Triple-decker: Interfacing atomistic-mesoscopic-continuum flow regimes. J. Comput. Phys. Dmitry A. Fedosov, George E. Karniadakis
2008	J	`jnl`	The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. J. Comput. Phys. Jasmine Foo, Xiaoliang Wan, George E. Karniadakis
2008	J	`jnl`	Velocity limit in DPD simulations of wall-bounded flows. J. Comput. Phys. Dmitry A. Fedosov, Igor Pivkin, George E. Karniadakis
2007	J	`jnl`	A Reconstruction Method for Gappy and Noisy Arterial Flow Data. IEEE Trans. Medical Imaging Alexander Yakhot, T. Anor, George E. Karniadakis
2007	J	`jnl`	NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications. Clust. Comput. Bruce M. Boghosian, Peter V. Coveney, Suchuan Dong, Lucas Finn, Shantenu Jha, George E. Karniadakis, Nicholas T. Karonis
2007	J	`jnl`	Runtime Visualization of the Human Arterial Tree. IEEE Trans. Vis. Comput. Graph. Joseph A. Insley, Michael E. Papka, Suchuan Dong, George E. Karniadakis, Nicholas T. Karonis
2007	J	`jnl`	Stochastic Computational Fluid Mechanics. Comput. Sci. Eng. Guang Lin, Xiaoliang Wan, Chau-Hsing Su, George E. Karniadakis
2007	J	`jnl`	Towards stable coupling methods for high-order discretization of fluid-structure interaction: Algorithms and observations. J. Comput. Phys. Robert M. Kirby, Zohar Yosibash, George E. Karniadakis
2006	J	`jnl`	A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications. J. Comput. Phys. Vasileios Symeonidis, George E. Karniadakis
2006	J	`jnl`	A sharp error estimate for the fast Gauss transform. J. Comput. Phys. Xiaoliang Wan, George E. Karniadakis
2006	J	`jnl`	Beyond Wiener-Askey Expansions: Handling Arbitrary PDFs. J. Sci. Comput. Xiaoliang Wan, George E. Karniadakis
2006	Misc	`conf`	Blood Flow at Arterial Branches: Complexities to Resolve for the Angioplasty Suite. International Conference on Computational Science (3) Peter Richardson, Igor Pivkin, George E. Karniadakis, David H. Laidlaw
2006	J	`jnl`	Foreword. J. Sci. Comput. David I. Gottlieb, Jan S. Hesthaven, George E. Karniadakis, Chi-Wang Shu
2006	J	`jnl`	Gappy data: To Krig or not to Krig? J. Comput. Phys. Hasan Gunes, Sirod Sirisup, George E. Karniadakis
2006	A	`conf`	Grid solutions for biological and physical cross-site simulations on the TeraGrid. IPDPS Suchuan Dong, Nicholas T. Karonis, George E. Karniadakis
2006	J	`jnl`	Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures. SIAM J. Sci. Comput. Xiaoliang Wan, George E. Karniadakis
2006	—	`conf`	NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications. CLADE Bruce M. Boghosian, Peter V. Coveney, Suchuan Dong, Lucas Finn, Shantenu Jha, George E. Karniadakis, Nicholas T. Karonis
2006	J	`jnl`	Numerical studies of the stochastic Korteweg-de Vries equation. J. Comput. Phys. Guang Lin, Leopold Grinberg, George E. Karniadakis
2006	A	`conf`	Poster reception - Human arterial tree simulation on TeraGrid. SC Leopold Grinberg, Suchuan Dong, James Noble, Alexander Yakhot, George E. Karniadakis, Nicholas T. Karonis
2006	J	`jnl`	Predicting shock dynamics in the presence of uncertainties. J. Comput. Phys. Guang Lin, Chau-Hsing Su, George E. Karniadakis
2006	J	`jnl`	Simulating and visualizing the human arterial system on the TeraGrid. Future Gener. Comput. Syst. Suchuan Dong, Joseph A. Insley, Nicholas T. Karonis, Michael E. Papka, Justin Binns, George E. Karniadakis
2006	J	`jnl`	Uncertainty quantification in simulation science. J. Comput. Phys. George E. Karniadakis, James Glimm
2005	J	`jnl`	A seamless approach to multiscale complex fluid simulation. Comput. Sci. Eng. Vasileios Symeonidis, George E. Karniadakis, Bruce Caswell
2005	J	`jnl`	Cross-site computations on the TeraGrid. Comput. Sci. Eng. Suchuan Dong, George E. Karniadakis, Nicholas T. Karonis
2005	J	`jnl`	Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems. J. Sci. Comput. Robert M. Kirby, George E. Karniadakis
2005	Misc	`conf`	Simulation and Visualization of Air Flow Around Bat Wings During Flight. International Conference on Computational Science (2) Igor Pivkin, Eduardo Hueso, Rachel Weinstein, David H. Laidlaw, Sharon Swartz, George E. Karniadakis
2005	J	`jnl`	Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows. J. Sci. Comput. Dongbin Xiu, Spencer J. Sherwin, Suchuan Dong, George E. Karniadakis
2004	J	`jnl`	Adaptive Generalized Polynomial Chaos for Nonlinear Random Oscillators. SIAM J. Sci. Comput. Didier Lucor, George E. Karniadakis
2004	J	`jnl`	Dual-level parallelism for high-order CFD methods. Parallel Comput. Suchuan Dong, George E. Karniadakis
2004	Misc	`conf`	Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes. International Conference on Computational Science Didier Lucor, Chau-Hsing Su, George E. Karniadakis
2004	J	`jnl`	Multilevel Parallelization Models in CFD. J. Aerosp. Comput. Inf. Commun. Suchuan Dong, George E. Karniadakis
2004	J	`jnl`	Particle Flurries: Synoptic 3D Pulsatile Flow Visualization. IEEE Computer Graphics and Applications Jason S. Sobel, Andrew S. Forsberg, David H. Laidlaw, Robert C. Zeleznik, Daniel F. Keefe, Igor Pivkin, George E. Karniadakis, Peter Richardson, Sharon Swartz
2004	—	`conf`	Simulation and visualization of flow around bat wings during flight. SIGGRAPH Posters Rachel Weinstein, Eduardo Hueso, Igor Pivkin, Sharon Swartz, David H. Laidlaw, George E. Karniadakis, Kenneth Breuer
2004	J	`jnl`	Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. SIAM J. Sci. Comput. Xiaoliang Wan, Dongbin Xiu, George E. Karniadakis
2004	A	`conf`	Visualization of Vortices in Simulated Airflow around Bat Wings During Flight. IEEE Visualization Eduardo Hueso, Igor Pivkin, Sharon Swartz, David H. Laidlaw, George E. Karniadakis, Kenny Breuer
2004	—	`conf`	Visualization of blood platelets in a virtual environment. SIGGRAPH Posters Igor Pivkin, Nicholas C. Yang, Peter Richardson, George E. Karniadakis, David H. Laidlaw
2003	—	`book`	Parallel Scientific Computing in C++ and MPI - A Seamless Approach to Parallel Algorithms and their Implementation. George E. Karniadakis, Robert M. Kirby
2003	Misc	`conf`	Performance Evaluation of Generalized Polynomial Chaos. International Conference on Computational Science Dongbin Xiu, Didier Lucor, Chau-Hsing Su, George E. Karniadakis
2002	J	`jnl`	A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. J. Sci. Comput. Jin Xu, Dongbin Xiu, George E. Karniadakis
2002	A	`conf`	Dual-level parallelism for deterministic and stochastic CFD problems. SC Suchuan Dong, George E. Karniadakis
2002	J	`jnl`	Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. J. Sci. Comput. M. Jardak, Chau-Hsing Su, George E. Karniadakis
2002	J	`jnl`	The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM J. Sci. Comput. Dongbin Xiu, George E. Karniadakis
2000	A	`conf`	Immersive virtual reality for visualizing flow through an artery. IEEE Visualization Andrew S. Forsberg, David H. Laidlaw, Andries van Dam, Robert M. Kirby, George E. Karniadakis, Jonathan L. Elion
1999	J	`jnl`	Basis Functions for Triangular and Quadrilateral High-Order Elements. SIAM J. Sci. Comput. Timothy C. Warburton, Spencer J. Sherwin, George E. Karniadakis
1999	A	`conf`	Direct Numerical Simulation of Turbulence with a PC/Linux Cluster: Fact or Fiction? SC George-Sosei Karamanos, Constantinos Evangelinos, Richard C. Boes, Robert M. Kirby, George E. Karniadakis
1997	J	`jnl`	Unsteady Two-Dimensional Flows in Complex Geometries: Comparative Bifurcation Studies with Global Eigenfunction Expansions. SIAM J. Sci. Comput. Anil K. Bangia, Paul F. Batcho, Ioannis G. Kevrekidis, George E. Karniadakis
1996	A	`conf`	Communication Performance Models in Prism : A Spectral Element-Fourier Parallel Navier-Stokes Solver. SC Constantinos Evangelinos, George E. Karniadakis
1996	J	`jnl`	Parallel Cfd Benchmarks on Cray Computers. Parallel Algorithms Appl. Constantinos Evangelinos, George E. Karniadakis