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ORCIDGeorge Em Karniadakis
George E. Karniadakis
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- affiliation: Brown University, Division of Applied Mathematics, Providence, RI, USA
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2020 – today
- 2024
[j210]Varun Kumar
, Somdatta Goswami, Daniel Smith, George Em Karniadakis:
Real-time prediction of gas flow dynamics in diesel engines using a deep neural operator framework. Appl. Intell. 54(11-12): 14-34 (2024)- [j209]Guansheng Li, He Li, Papa Alioune Ndour, Mélanie Franco, Xuejin Li, Ian Macdonald, Ming Dao, Pierre A. Buffet, George Em Karniadakis:
Red blood cell passage through deformable interendothelial slits in the spleen: Insights into splenic filtration and hemodynamics. Comput. Biol. Medicine 182: 109198 (2024) - [j208]Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Nicholas Plewacki, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis:
Deep neural operators as accurate surrogates for shape optimization. Eng. Appl. Artif. Intell. 129: 107615 (2024) - [j207]Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, George Em Karniadakis:
Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks. Eng. Appl. Artif. Intell. 138: 109378 (2024) - [j206]Sathesh Mariappan, Kamaljyoti Nath, George Em Karniadakis:
Learning thermoacoustic interactions in combustors using a physics-informed neural network. Eng. Appl. Artif. Intell. 138: 109388 (2024) - [j205]Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan:
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. J. Comput. Phys. 505: 112917 (2024) - [j204]Zongren Zou, Xuhui Meng, George Em Karniadakis:
Correcting model misspecification in physics-informed neural networks (PINNs). J. Comput. Phys. 505: 112918 (2024) - [j203]Qianying Cao, Somdatta Goswami, George Em Karniadakis:
Laplace neural operator for solving differential equations. Nat. Mac. Intell. 6(6): 631-640 (2024) - [j202]Alan John Varghese, Aniruddha Bora, Mengjia Xu, George Em Karniadakis:
TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers. Neural Networks 172: 106086 (2024) - [j201]Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi:
Tackling the curse of dimensionality with physics-informed neural networks. Neural Networks 176: 106369 (2024) - [j200]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): 161-190 (2024) - [j199]Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis:
Leveraging Multitime Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. SIAM J. Sci. Comput. 46(2): 216- (2024) - [j198]Shengze Cai, Callum Gray, George Em Karniadakis:
Physics-Informed Neural Networks Enhanced Particle Tracking Velocimetry: An Example for Turbulent Jet Flow. IEEE Trans. Instrum. Meas. 73: 1-9 (2024) - [j197]Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis:
DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs. IEEE Trans. Neural Networks Learn. Syst. 35(1): 985-998 (2024) - [c28]Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen:
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks. IJCNN 2024: 1-8 - [c27]Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis:
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. L4DC 2024: 1-12 - [c26]Bradley H. Theilman, Qian Zhang, Adar Kahana, Eric C. Cyr, Nathaniel Trask, James B. Aimone, George Em Karniadakis:
Spiking Physics-Informed Neural Networks on Loihi 2. NICE 2024: 1-6 - [i161]Mario De Florio, Adar Kahana, George Em Karniadakis:
Analysis of biologically plausible neuron models for regression with spiking neural networks. CoRR abs/2401.00369 (2024) - [i160]Alena Kopanicáková, George Em Karniadakis:
DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations. CoRR abs/2401.02016 (2024) - [i159]Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap, George Em Karniadakis:
RiemannONets: Interpretable Neural Operators for Riemann Problems. CoRR abs/2401.08886 (2024) - [i158]Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi:
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations. CoRR abs/2402.07465 (2024) - [i157]Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis:
Two-scale Neural Networks for Partial Differential Equations with Small Parameters. CoRR abs/2402.17232 (2024) - [i156]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 abs/2403.13299 (2024) - [i155]Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, George Em Karniadakis:
Learning in PINNs: Phase transition, total diffusion, and generalization. CoRR abs/2403.18494 (2024) - [i154]Taorui Wang, Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis:
Tensor neural networks for high-dimensional Fokker-Planck equations. CoRR abs/2404.05615 (2024) - [i153]Zongren Zou, Tingwei Meng, Paula X. Chen, Jérôme Darbon, George Em Karniadakis:
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning. CoRR abs/2404.08809 (2024) - [i152]Shupeng Wang, George Em Karniadakis:
GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains. CoRR abs/2405.00217 (2024) - [i151]Zongren Zou, Adar Kahana, Enrui Zhang, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis:
Large scale scattering using fast solvers based on neural operators. CoRR abs/2405.12380 (2024) - [i150]Benjamin Shih, Ahmad Peyvan, Zhongqiang Zhang, George Em Karniadakis:
Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity. CoRR abs/2405.19166 (2024) - [i149]Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang, Zongren Zou, George Em Karniadakis:
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks. CoRR abs/2406.02917 (2024) - [i148]Youngkyu Lee, Alena Kopanicáková, George Em Karniadakis:
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications. CoRR abs/2406.10997 (2024) - [i147]Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi:
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations. CoRR abs/2406.11676 (2024) - [i146]Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis:
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks. CoRR abs/2406.11708 (2024) - [i145]Juan Diego Toscano, Theo Käufer, Zhibo Wang, Martin Maxey, Christian Cierpka, George Em Karniadakis:
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks. CoRR abs/2407.15727 (2024) - [i144]Khemraj Shukla, Zongren Zou, Chi Hin Chan, Additi Pandey, Zhicheng Wang, George Em Karniadakis:
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements. CoRR abs/2407.21217 (2024) - [i143]Varun Kumar, Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis:
Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving. CoRR abs/2408.02198 (2024) - [i142]Mario De Florio, Zongren Zou, Daniele E. Schiavazzi, George Em Karniadakis:
Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology. CoRR abs/2408.07201 (2024) - [i141]Alan John Varghese, Zhen Zhang, George Em Karniadakis:
SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification. CoRR abs/2408.16698 (2024) - [i140]Maziar Raissi, Paris Perdikaris, Nazanin Ahmadi Daryakenari, George Em Karniadakis:
Physics-Informed Neural Networks and Extensions. CoRR abs/2408.16806 (2024) - [i139]Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan:
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. CoRR abs/2409.01124 (2024) - [i138]Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen, Kenji Kawaguchi, George Em Karniadakis:
State-space models are accurate and efficient neural operators for dynamical systems. CoRR abs/2409.03231 (2024) - [i137]Vivek Oommen, Aniruddha Bora, Zhen Zhang, George Em Karniadakis:
Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling. CoRR abs/2409.08477 (2024) - [i136]Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis:
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models. CoRR abs/2409.09614 (2024) - [i135]Nazanin Ahmadi Daryakenari, Shupeng Wang, George Em Karniadakis:
CMINNs: Compartment Model Informed Neural Networks - Unlocking Drug Dynamics. CoRR abs/2409.12998 (2024) - 2023
- [j196]Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi:
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. Eng. Appl. Artif. Intell. 126: 107183 (2023) - [j195]Patricio Clark Di Leoni, Lu Lu, Charles Meneveau, George Em Karniadakis, Tamer A. Zaki:
Neural operator prediction of linear instability waves in high-speed boundary layers. J. Comput. Phys. 474: 111793 (2023) - [j194]Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis:
Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. J. Comput. Phys. 477: 111902 (2023) - [j193]Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis:
On the influence of over-parameterization in manifold based surrogates and deep neural operators. J. Comput. Phys. 479: 112008 (2023) - [j192]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: 112310 (2023) - [j191]QiZhi He, Mauro Perego, Amanda A. Howard, George Em Karniadakis, Panos Stinis:
A hybrid deep neural operator/finite element method for ice-sheet modeling. J. Comput. Phys. 492: 112428 (2023) - [j190]Amanda A. Howard, Mauro Perego, George Em Karniadakis, Panos Stinis:
Multifidelity deep operator networks for data-driven and physics-informed problems. J. Comput. Phys. 493: 112462 (2023) - [j189]Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, Robert M. Kirby:
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions. J. Comput. Phys. 493: 112464 (2023) - [j188]Yue Hao, Patricio Clark Di Leoni, Olaf Marxen, Charles Meneveau, George Em Karniadakis, Tamer A. Zaki:
Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators. J. Comput. Sci. 73: 102120 (2023) - [j187]Yeonjong Shin, Jérôme Darbon, George Em Karniadakis:
Accelerating gradient descent and Adam via fractional gradients. Neural Networks 161: 185-201 (2023) - [j186]Guansheng Li, Yuhao Qiang, He Li, Xuejin Li, Pierre Buffet, Ming Dao, George Em Karniadakis:
A combined computational and experimental investigation of the filtration function of splenic macrophages in sickle cell disease. PLoS Comput. Biol. 19(12) (2023) - [j185]Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis:
Learning Poisson Systems and Trajectories of Autonomous Systems via Poisson Neural Networks. IEEE Trans. Neural Networks Learn. Syst. 34(11): 8271-8283 (2023) - [i134]Zongren Zou, George Em Karniadakis:
L-HYDRA: Multi-Head Physics-Informed Neural Networks. CoRR abs/2301.02152 (2023) - [i133]QiZhi He, Mauro Perego, Amanda A. Howard, George Em Karniadakis, Panos Stinis:
A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling. CoRR abs/2301.11402 (2023) - [i132]Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis:
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils. CoRR abs/2302.00807 (2023) - [i131]Aniruddha Bora, Khemraj Shukla, Shixuan Zhang, Bryce Harrop, Ruby Leung, George Em Karniadakis:
Learning bias corrections for climate models using deep neural operators. CoRR abs/2302.03173 (2023) - [i130]Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee, Bryan T. Susi, George Em Karniadakis:
Learning stiff chemical kinetics using extended deep neural operators. CoRR abs/2302.12645 (2023) - [i129]Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, Robert M. Kirby:
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions. CoRR abs/2302.14227 (2023) - [i128]Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen:
Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks. CoRR abs/2303.02243 (2023) - [i127]Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, George Em Karniadakis:
ViTO: Vision Transformer-Operator. CoRR abs/2303.08891 (2023) - [i126]Qianying Cao, Somdatta Goswami, George Em Karniadakis:
LNO: Laplace Neural Operator for Solving Differential Equations. CoRR abs/2303.10528 (2023) - [i125]Lei Ma, Rong xin Li, Fanhai Zeng, Ling Guo, George Em Karniadakis:
Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs. CoRR abs/2303.10913 (2023) - [i124]Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis:
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. CoRR abs/2303.12928 (2023) - [i123]Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, Michael D. Shields:
Learning in latent spaces improves the predictive accuracy of deep neural operators. CoRR abs/2304.07599 (2023) - [i122]Simin Shekarpaz, Fanhai Zeng, George Em Karniadakis:
Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models. CoRR abs/2304.13205 (2023) - [i121]Kamaljyoti Nath, Xuhui Meng, Daniel J. Smith, George Em Karniadakis:
Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines. CoRR abs/2304.13799 (2023) - [i120]Minglang Yin, Zongren Zou, Enrui Zhang, Cristina Cavinato, Jay D. Humphrey, George Em Karniadakis:
A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes. CoRR abs/2305.03184 (2023) - [i119]Elham Kiyani, Khemraj Shukla, George Em Karniadakis, Mikko Karttunen:
A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data. CoRR abs/2305.10706 (2023) - [i118]Chayan Banerjee, Kien Nguyen, Clinton Fookes, George Em Karniadakis:
Physics-Informed Computer Vision: A Review and Perspectives. CoRR abs/2305.18035 (2023) - [i117]Ehsan Haghighat, Umair bin Waheed, George Em Karniadakis:
A novel deeponet model for learning moving-solution operators with applications to earthquake hypocenter localization. CoRR abs/2306.04096 (2023) - [i116]Varun Kumar, Leonard Gleyzer, Adar Kahana, Khemraj Shukla, George Em Karniadakis:
CrunchGPT: A chatGPT assisted framework for scientific machine learning. CoRR abs/2306.15551 (2023) - [i115]Alena Kopanicáková, Hardik Kothari, George Em Karniadakis, Rolf Krause:
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. CoRR abs/2306.17648 (2023) - [i114]Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, George Em Karniadakis:
Residual-based attention and connection to information bottleneck theory in PINNs. CoRR abs/2307.00379 (2023) - [i113]Alan John Varghese, Aniruddha Bora, Mengjia Xu, George Em Karniadakis:
TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers. CoRR abs/2307.02588 (2023) - [i112]Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis:
Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression. CoRR abs/2307.08107 (2023) - [i111]Oded Ovadia, Eli Turkel, Adar Kahana, George Em Karniadakis:
DiTTO: Diffusion-inspired Temporal Transformer Operator. CoRR abs/2307.09072 (2023) - [i110]Elham Kiyani, Mahdi Kooshkbaghi, Khemraj Shukla, Rahul Babu Koneru, Zhen Li, Luis Bravo, Anindya Ghoshal, George Em Karniadakis, Mikko Karttunen:
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs. CoRR abs/2307.09142 (2023) - [i109]Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi:
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks. CoRR abs/2307.12306 (2023) - [i108]Nikolas Borrel-Jensen, Somdatta Goswami, Allan P. Engsig-Karup, George Em Karniadakis, Cheol-Ho Jeong:
Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators. CoRR abs/2308.05141 (2023) - [i107]Qian Zhang, Chenxi Wu, Adar Kahana, Youngeun Kim, Yuhang Li, George Em Karniadakis, Priyadarshini Panda:
Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning. CoRR abs/2308.16372 (2023) - [i106]Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla, George Em Karniadakis:
AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification. CoRR abs/2310.01433 (2023) - [i105]Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen:
DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks. CoRR abs/2310.02491 (2023) - [i104]Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, George Em Karniadakis:
Learning characteristic parameters and dynamics of centrifugal pumps under multi-phase flow using physics-informed neural networks. CoRR abs/2310.03001 (2023) - [i103]Zongren Zou, Xuhui Meng, George Em Karniadakis:
Correcting model misspecification in physics-informed neural networks (PINNs). CoRR abs/2310.10776 (2023) - [i102]Bin Lin, Zhiping Mao, Zhicheng Wang, George Em Karniadakis:
Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions. CoRR abs/2310.19590 (2023) - [i101]Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis:
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. CoRR abs/2311.07790 (2023) - [i100]Zongren Zou, Xuhui Meng, George Em Karniadakis:
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators. CoRR abs/2311.11262 (2023) - [i99]Hanxun Jin, Enrui Zhang, Boyu Zhang, Sridhar Krishnaswamy, George Em Karniadakis, Horacio D. Espinosa:
Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operators. CoRR abs/2311.13812 (2023) - [i98]Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, Kenji Kawaguchi:
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs. CoRR abs/2311.15283 (2023) - [i97]Chenxi Wu, Alan John Varghese, Vivek Oommen, George Em Karniadakis:
GPT vs Human for Scientific Reviews: A Dual Source Review on Applications of ChatGPT in Science. CoRR abs/2312.03769 (2023) - [i96]Vivek Oommen, Khemraj Shukla, Saaketh Desai, Rémi Dingreville, George Em Karniadakis:
Rethinking materials simulations: Blending direct numerical simulations with neural operators. CoRR abs/2312.05410 (2023) - [i95]Mario De Florio, Ioannis G. Kevrekidis, George Em Karniadakis:
AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression. CoRR abs/2312.14237 (2023) - [i94]Zheyuan Hu, Zekun Shi, George Em Karniadakis, Kenji Kawaguchi:
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks. CoRR abs/2312.14499 (2023) - 2022
- [j184]Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis:
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. Neurocomputing 468: 165-180 (2022) - [j183]Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis, George Em Karniadakis:
Learning functional priors and posteriors from data and physics. J. Comput. Phys. 457: 111073 (2022) - [j182]Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis:
Meta-learning PINN loss functions. J. Comput. Phys. 458: 111121 (2022) - [j181]Yue Zhao, Zhiping Mao, Ling Guo, Yifa Tang, George Em Karniadakis:
A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. J. Comput. Phys. 461: 111213 (2022) - [j180]Ameya D. Jagtap, Zhiping Mao, Nikolaus A. Adams, George Em Karniadakis:
Physics-informed neural networks for inverse problems in supersonic flows. J. Comput. Phys. 466: 111402 (2022) - [j179]Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis:
Deep transfer operator learning for partial differential equations under conditional shift. Nat. Mac. Intell. 4(12): 1155-1164 (2022) - [j178]Ethan Pickering, Stephen Guth, George Em Karniadakis, Themistoklis P. Sapsis:
Discovering and forecasting extreme events via active learning in neural operators. Nat. Comput. Sci. 2(12): 823-833 (2022) - [j177]Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis:
Approximation rates of DeepONets for learning operators arising from advection-diffusion equations. Neural Networks 153: 411-426 (2022) - [j176]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) - [j175]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) - [j174]Enrui Zhang, Bart Spronck, Jay D. Humphrey, George Em Karniadakis:
G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning. PLoS Comput. Biol. 18(10): 1010660 (2022) - [j173]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): 80- (2022) - [j172]Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi:
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? SIAM J. Sci. Comput. 44(5): 3158- (2022) - [j171]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): 1341- (2022) - [j170]Khemraj Shukla, Ameya D. Jagtap, James L. Blackshire, Daniel Sparkman, George Em Karniadakis:
A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems. IEEE Signal Process. Mag. 39(1): 68-77 (2022) - [j169]Liu Yang, George Em Karniadakis:
Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models. IEEE Trans. Neural Networks Learn. Syst. 33(2): 528-538 (2022) - [i93]Tingwei Meng, Zhen Zhang, Jérôme Darbon, George Em Karniadakis:
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems. CoRR abs/2201.05475 (2022) - [i92]Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis:
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons. CoRR abs/2201.07766 (2022) - [i91]Mitchell Daneker, Zhen Zhang, George Em Karniadakis, Lu Lu:
Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks. CoRR abs/2202.01723 (2022) - [i90]Ameya D. Jagtap, Dimitrios Mitsotakis, George Em Karniadakis:
Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations. CoRR abs/2202.02899 (2022) - [i89]Marta D'Elia, Hang Deng, Cedric G. Fraces, Krishna C. Garikipati, Lori Graham-Brady, Amanda A. Howard, George Em Karniadakis, Vahid Keshavarzzadeh, Robert M. Kirby, J. Nathan Kutz, Chunhui Li, Xing Liu, Hannah Lu, Pania Newell, Daniel O'Malley, Masa Prodanovic, Gowri Srinivasan, Alexandre M. Tartakovsky, Daniel M. Tartakovsky, Hamdi A. Tchelepi, Bozo Vazic, Hari S. Viswanathan, Hongkyu Yoon, Piotr Zarzycki:
Machine Learning in Heterogeneous Porous Materials. CoRR abs/2202.04137 (2022) - [i88]Ameya D. Jagtap, Zhiping Mao, Nikolaus A. Adams, George Em Karniadakis:
Physics-informed neural networks for inverse problems in supersonic flows. CoRR abs/2202.11821 (2022) - [i87]Minglang Yin, Enrui Zhang, Yue Yu, George Em Karniadakis:
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems. CoRR abs/2203.00003 (2022) - [i86]Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis:
On the influence of over-parameterization in manifold based surrogates and deep neural operators. CoRR abs/2203.05071 (2022) - [i85]Ethan Pickering, George Em Karniadakis, Themistoklis P. Sapsis:
Discovering and forecasting extreme events via active learning in neural operators. CoRR abs/2204.02488 (2022) - [i84]Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Rémi Dingreville, George Em Karniadakis:
Learning two-phase microstructure evolution using neural operators and autoencoder architectures. CoRR abs/2204.07230 (2022) - [i83]Amanda A. Howard, Mauro Perego, George E. Karniadakis, Panos Stinis:
Multifidelity Deep Operator Networks. CoRR abs/2204.09157 (2022) - [i82]Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis:
Deep transfer learning for partial differential equations under conditional shift with DeepONet. CoRR abs/2204.09810 (2022) - [i81]Somdatta Goswami, David S. Li, Bruno V. Rego, Marcos Latorre, Jay D. Humphrey, George Em Karniadakis:
Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms. CoRR abs/2205.03780 (2022) - [i80]Kevin Linka, Amelie Schäfer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl:
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems. CoRR abs/2205.08304 (2022) - [i79]Khemraj Shukla, Mengjia Xu, Nathaniel Trask, George Em Karniadakis:
Scalable algorithms for physics-informed neural and graph networks. CoRR abs/2205.08332 (2022) - [i78]Adar Kahana, Qian Zhang, Leonard Gleyzer, George Em Karniadakis:
Function Regression using Spiking DeepONet. CoRR abs/2205.10130 (2022) - [i77]Min Cai, George Em Karniadakis, Changpin Li:
Fractional SEIR Model and Data-Driven Predictions of COVID-19 Dynamics of Omicron Variant. CoRR abs/2205.11379 (2022) - [i76]Somdatta Goswami, Aniruddha Bora, Yue Yu, George Em Karniadakis:
Physics-Informed Deep Neural Operator Networks. CoRR abs/2207.05748 (2022) - [i75]Enrui Zhang, Bart Spronck, Jay D. Humphrey, George Em Karniadakis:
G2Φnet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learning. CoRR abs/2208.09889 (2022) - [i74]Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George Em Karniadakis:
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators. CoRR abs/2208.11866 (2022) - [i73]Enrui Zhang, Adar Kahana, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis:
A Hybrid Iterative Numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods. CoRR abs/2208.13273 (2022) - [i72]Ameya D. Jagtap, George Em Karniadakis:
How important are activation functions in regression and classification? A survey, performance comparison, and future directions. CoRR abs/2209.02681 (2022) - [i71]Adar Kahana, Enrui Zhang, Somdatta Goswami, George Em Karniadakis, Rishikesh Ranade, Jay Pathak:
On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations. CoRR abs/2210.17392 (2022) - [i70]Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi:
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. CoRR abs/2211.08939 (2022) - [i69]Qian Zhang, Adar Kahana, George Em Karniadakis, Panos Stinis:
SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations. CoRR abs/2211.09928 (2022) - [i68]Ahmad Peyvan, Khemraj Shukla, Jesse Chan, George Em Karniadakis:
High-Order Methods for Hypersonic Flows with Strong Shocks and Real Chemistry. CoRR abs/2211.12635 (2022) - [i67]Min Zhu, Handi Zhang, Anran Jiao, George Em Karniadakis, Lu Lu:
Reliable extrapolation of deep neural operators informed by physics or sparse observations. CoRR abs/2212.06347 (2022) - 2021
- [j168]Max Carlson, Xiaoning Zheng, Hari Sundar, George Em Karniadakis, Robert M. Kirby:
An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains. Comput. Phys. Commun. 261: 107695 (2021) - [j167]Fangying Song, George Em Karniadakis:
Variable-Order Fractional Models for Wall-Bounded Turbulent Flows. Entropy 23(6): 782 (2021) - [j166]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) - [j165]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) - [j164]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) - [j163]Zhicheng Wang, Xiaoning Zheng, Chryssostomos Chryssostomidis, George Em Karniadakis:
A phase-field method for boiling heat transfer. J. Comput. Phys. 435: 110239 (2021) - [j162]Shengze Cai, Zhicheng Wang, Lu Lu, Tamer A. Zaki, George Em Karniadakis:
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks. J. Comput. Phys. 436: 110296 (2021) - [j161]Xuhui Meng, Hessam Babaee, George Em Karniadakis:
Multi-fidelity Bayesian neural networks: Algorithms and applications. J. Comput. Phys. 438: 110361 (2021) - [j160]Qin Lou, Xuhui Meng, George Em Karniadakis:
Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. J. Comput. Phys. 447: 110676 (2021) - [j159]Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis:
Parallel physics-informed neural networks via domain decomposition. J. Comput. Phys. 447: 110683 (2021) - [j158]Zhiping Mao, Lu Lu, Olaf Marxen, Tamer A. Zaki, George Em Karniadakis:
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. J. Comput. Phys. 447: 110698 (2021) - [j157]Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, George Em Karniadakis:
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3(3): 218-229 (2021) - [j156]Ehsan Kharazmi, Min Cai, Xiaoning Zheng, Zhen Zhang, Guang Lin, George Em Karniadakis:
Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks. Nat. Comput. Sci. 1(11): 744-753 (2021) - [j155]Yixiang Deng, Lu Lu, Laura Aponte, Angeliki M. Angelidi, Vera Novak, George Em Karniadakis, Christos S. Mantzoros:
Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. npj Digit. Medicine 4 (2021) - [j154]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) - [j153]He Li, Zixiang Leonardo Liu, Lu Lu, Pierre Buffet, George Em Karniadakis:
How the spleen reshapes and retains young and old red blood cells: A computational investigation. PLoS Comput. Biol. 17(11) (2021) - [j152]Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis:
DeepXDE: A Deep Learning Library for Solving Differential Equations. SIAM Rev. 63(1): 208-228 (2021) - [j151]Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis:
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-Informed Neural Networks. SIAM J. Sci. Comput. 43(3): B811-B830 (2021) - [c25]Ameya D. Jagtap, George E. Karniadakis:
Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations. AAAI Spring Symposium: MLPS 2021 - [i66]Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis:
Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation. CoRR abs/2101.02355 (2021) - [i65]Liu Yang, Tingwei Meng, George Em Karniadakis:
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates. CoRR abs/2101.06802 (2021) - [i64]Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis:
Error estimates for DeepOnets: A deep learning framework in infinite dimensions. CoRR abs/2102.09618 (2021) - [i63]Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis:
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations. CoRR abs/2102.10621 (2021) - [i62]Yeonjong Shin, Jérôme Darbon, George Em Karniadakis:
A Caputo fractional derivative-based algorithm for optimization. CoRR abs/2104.02259 (2021) - [i61]Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis:
Parallel Physics-Informed Neural Networks via Domain Decomposition. CoRR abs/2104.10013 (2021) - [i60]Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, George Em Karniadakis:
Physics-informed neural networks (PINNs) for fluid mechanics: A review. CoRR abs/2105.09506 (2021) - [i59]Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis:
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. CoRR abs/2105.09513 (2021) - [i58]Qian Zhang, Konstantina Sampani, Mengjia Xu, Shengze Cai, Yixiang Deng, He Li, Jennifer K. Sun, George Em Karniadakis:
AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images. CoRR abs/2106.02800 (2021) - [i57]Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis, George Em Karniadakis:
Learning Functional Priors and Posteriors from Data and Physics. CoRR abs/2106.05863 (2021) - [i56]Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis:
Meta-learning PINN loss functions. CoRR abs/2107.05544 (2021) - [i55]Somdatta Goswami, Minglang Yin, Yue Yu, George E. Karniadakis:
A physics-informed variational DeepONet for predicting the crack path in brittle materials. CoRR abs/2108.06905 (2021) - [i54]Minglang Yin, Ehsan Ban, Bruno V. Rego, Enrui Zhang, Cristina Cavinato, Jay D. Humphrey, George Em Karniadakis:
Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network. CoRR abs/2108.11985 (2021) - [i53]Zhen Zhang, Yeonjong Shin, George Em Karniadakis:
GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems. CoRR abs/2109.00092 (2021) - [i52]Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi:
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? CoRR abs/2109.09444 (2021) - [i51]Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis:
DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs. CoRR abs/2109.13441 (2021) - [i50]Jeremy Yu, Lu Lu, Xuhui Meng, George Em Karniadakis:
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. CoRR abs/2111.02801 (2021) - 2020
- [j150]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) - [j149]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) - [j148]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) - [j147]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) - [j146]Qiang Zheng, Lingzao Zeng, George Em Karniadakis:
Physics-informed semantic inpainting: Application to geostatistical modeling. J. Comput. Phys. 419: 109676 (2020) - [j145]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) - [j144]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) - [j143]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) - [j142]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) - [j141]Alireza Yazdani, Lu Lu, Maziar Raissi, George Em Karniadakis:
Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput. Biol. 16(11) (2020) - [j140]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) - [j139]Dongkun Zhang, Ling Guo, George Em Karniadakis:
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. SIAM J. Sci. Comput. 42(2): A639-A665 (2020) - [c24]Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis:
DeepXDE: A Deep Learning Library for Solving Differential Equations. AAAI Spring Symposium: MLPS 2020 - [c23]Marta D'Elia, George E. Karniadakis, Guofei Pang, Michael L. Parks:
Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models. AAAI Spring Symposium: MLPS 2020 - [i49]Pengzhan Jin, Aiqing Zhu, George Em Karniadakis, Yifa Tang:
Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems. CoRR abs/2001.03750 (2020) - [i48]Dixia Fan, Liu Yang, Michael S. Triantafyllou, George Em Karniadakis:
Reinforcement Learning for Active Flow Control in Experiments. CoRR abs/2003.03419 (2020) - [i47]Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis:
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition. CoRR abs/2003.05385 (2020) - [i46]Liu Yang, Xuhui Meng, George Em Karniadakis:
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data. CoRR abs/2003.06097 (2020) - [i45]Yeonjong Shin, Jérôme Darbon, George Em Karniadakis:
On the Convergence and generalization of Physics Informed Neural Networks. CoRR abs/2004.01806 (2020) - [i44]Guofei Pang, Marta D'Elia, Michael L. Parks, George E. Karniadakis:
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications. CoRR abs/2004.04276 (2020) - [i43]Khemraj Shukla, Patricio Clark Di Leoni, James L. Blackshire, Daniel Sparkman, George Em Karniadakis:
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks. CoRR abs/2005.03596 (2020) - [i42]Hui Zhang, Fanhai Zeng, Xiaoyun Jiang, George Em Karniadakis:
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. CoRR abs/2007.07015 (2020) - [i41]Liu Yang, Constantinos Daskalakis, George Em Karniadakis:
Generative Ensemble-Regression: Learning Stochastic Dynamics from Discrete Particle Ensemble Observations. CoRR abs/2008.01915 (2020) - [i40]Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis:
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks. CoRR abs/2008.10653 (2020) - [i39]Enrui Zhang, Minglang Yin, George Em Karniadakis:
Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging. CoRR abs/2009.04525 (2020) - [i38]Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis:
Error estimates of residual minimization using neural networks for linear PDEs. CoRR abs/2010.08019 (2020) - [i37]Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis:
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks. CoRR abs/2012.03133 (2020) - [i36]Xuhui Meng, Hessam Babaee, George Em Karniadakis:
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications. CoRR abs/2012.13294 (2020)
2010 – 2019
- 2019
- [j138]Fangying Song, George E. Karniadakis:
Fractional magneto-hydrodynamics: Algorithms and applications. J. Comput. Phys. 378: 44-62 (2019) - [j137]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) - [j136]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) - [j135]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) - [j134]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) - [j133]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) - [j132]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) - [j131]Dixia Fan, Gurvan Jodin, Thomas Consi, L. Bonfiglio, Y. Ma, Elizabeth Keyes, George E. Karniadakis, Michael S. Triantafyllou:
A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics. Sci. Robotics 4(36) (2019) - [j130]Nan Wang, Zhiping Mao, Chengming Huang, George E. Karniadakis:
A Spectral Penalty Method for Two-Sided Fractional Differential Equations with General Boundary Conditions. SIAM J. Sci. Comput. 41(3): A1840-A1866 (2019) - [j129]Mamikon A. Gulian, Maziar Raissi, Paris Perdikaris, George E. Karniadakis:
Machine Learning of Space-Fractional Differential Equations. SIAM J. Sci. Comput. 41(4): A2485-A2509 (2019) - [j128]Ling Guo, Fanhai Zeng, Ian W. Turner, Kevin Burrage, George Em Karniadakis:
Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations. SIAM J. Sci. Comput. 41(4): A2510-A2535 (2019) - [j127]Guofei Pang, Lu Lu, George Em Karniadakis:
fPINNs: Fractional Physics-Informed Neural Networks. SIAM J. Sci. Comput. 41(4): A2603-A2626 (2019) - [c22]Liu Yang, Prabhat, George E. Karniadakis, Sean Treichler, Thorsten Kurth, Keno Fischer, David A. Barajas-Solano, Joshua Romero, Valentin Churavy, Alexandre M. Tartakovsky, Michael Houston:
Highly-Ccalable, Physics-Informed GANs for Learning Solutions of Stochastic PDEs. DLS@SC 2019: 1-11 - [i35]Lu Lu, Yeonjong Shin, Yanhui Su, George E. Karniadakis:
Dying ReLU and Initialization: Theory and Numerical Examples. CoRR abs/1903.06733 (2019) - [i34]Dongkun Zhang, Ling Guo, George E. Karniadakis:
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. CoRR abs/1905.01205 (2019) - [i33]Pengzhan Jin, Lu Lu, Yifa Tang, George E. Karniadakis:
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. CoRR abs/1905.11427 (2019) - [i32]Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis:
DeepXDE: A deep learning library for solving differential equations. CoRR abs/1907.04502 (2019) - [i31]Yeonjong Shin, George E. Karniadakis:
Trainability and Data-dependent Initialization of Over-parameterized ReLU Neural Networks. CoRR abs/1907.09696 (2019) - [i30]Liu Yang, George E. Karniadakis:
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models. CoRR abs/1908.11462 (2019) - [i29]Qiang Zheng, Lingzao Zeng, George E. Karniadakis:
Physics-informed semantic inpainting: Application to geostatistical modeling. CoRR abs/1909.09459 (2019) - [i28]Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis:
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs. CoRR abs/1909.10145 (2019) - [i27]Ameya D. Jagtap, Kenji Kawaguchi, George E. Karniadakis:
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks. CoRR abs/1909.12228 (2019) - [i26]Lu Lu, Pengzhan Jin, George Em Karniadakis:
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. CoRR abs/1910.03193 (2019) - [i25]Xiaoli Chen, Jinqiao Duan, George Em Karniadakis:
Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements. CoRR abs/1910.09098 (2019) - [i24]Liu Yang, Sean Treichler, Thorsten Kurth, Keno Fischer, David A. Barajas-Solano, Joshua Romero, Valentin Churavy, Alexandre M. Tartakovsky, Michael Houston, Prabhat, George E. Karniadakis:
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs. CoRR abs/1910.13444 (2019) - [i23]Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis:
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations. CoRR abs/1912.00873 (2019) - [i22]José del Águila Ferrandis, Michael S. Triantafyllou, Chryssostomos Chryssostomidis, George Em Karniadakis:
Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states. CoRR abs/1912.13382 (2019) - 2018
- [j126]Zhen Li, Xin Bian, Yu-Hang Tang, George E. Karniadakis:
A dissipative particle dynamics method for arbitrarily complex geometries. J. Comput. Phys. 355: 534-547 (2018) - [j125]Maziar Raissi, George E. Karniadakis:
Hidden physics models: Machine learning of nonlinear partial differential equations. J. Comput. Phys. 357: 125-141 (2018) - [j124]Lifei Zhao, Zhen Li, Bruce Caswell, Jie Ouyang, George E. Karniadakis:
Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows. J. Comput. Phys. 363: 116-127 (2018) - [j123]Dongkun Zhang, Liu Yang, George E. Karniadakis:
Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors. J. Comput. Phys. 374: 121-134 (2018) - [j122]Zhiping Mao, George E. Karniadakis:
A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative. SIAM J. Numer. Anal. 56(1): 24-49 (2018) - [j121]Zhijiang Zhang, Weihua Deng, George E. Karniadakis:
A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian. SIAM J. Numer. Anal. 56(5): 3010-3039 (2018) - [j120]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]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: 485-508 (2015) - [j82]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) - [j81]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): 153-183 (2015) - [j80]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): 2074-2096 (2015) - [j79]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) - [j78]Mengdi Zheng, George E. Karniadakis:
Numerical Methods for SPDEs with Tempered Stable Processes. SIAM J. Sci. Comput. 37(3) (2015) - [j77]Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis:
Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions. SIAM J. Sci. Comput. 37(4) (2015) - [j76]Mohsen Zayernouri, Mark Ainsworth, George E. Karniadakis:
Tempered Fractional Sturm-Liouville EigenProblems. SIAM J. Sci. Comput. 37(4) (2015) - [j75]Mengdi Zheng, Boris L. Rozovsky, George E. Karniadakis:
Adaptive Wick-Malliavin Approximation to Nonlinear SPDEs with Discrete Random Variables. SIAM J. Sci. Comput. 37(4) (2015) - [j74]Heyrim Cho, Xiu Yang, Daniele Venturi, George E. Karniadakis:
Algorithms for Propagating Uncertainty Across Heterogeneous Domains. SIAM J. Sci. Comput. 37(6) (2015) - [j73]Fanhai Zeng, Zhongqiang Zhang, George E. Karniadakis:
A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations. SIAM J. Sci. Comput. 37(6) (2015) - [j72]Zheng Zhang, Xiu Yang, Ivan V. Oseledets, George E. Karniadakis, Luca Daniel:
Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 34(1): 63-76 (2015) - [c21]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: 2:1-2:12 - [i5]Zhen Li, Yu-Hang Tang, Xuejin Li, George E. Karniadakis:
Mesoscale modeling of phase transition dynamics of thermoresponsive polymers. CoRR abs/1504.07094 (2015) - 2014
- [j71]Yu-Hang Tang, George E. Karniadakis:
Accelerating dissipative particle dynamics simulations on GPUs: Algorithms, numerics and applications. Comput. Phys. Commun. 185(11): 2809-2822 (2014) - [j70]Mohsen Zayernouri, George E. Karniadakis:
Exponentially accurate spectral and spectral element methods for fractional ODEs. J. Comput. Phys. 257: 460-480 (2014) - [j69]Suchuan Dong, George E. Karniadakis, Chryssostomos Chryssostomidis:
A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. 261: 83-105 (2014) - [j68]Zhen Li, Yu-Hang Tang, Huan Lei, Bruce Caswell, George E. Karniadakis:
Energy-conserving dissipative particle dynamics with temperature-dependent properties. J. Comput. Phys. 265: 113-127 (2014) - [j67]Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis:
On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations. J. Comput. Phys. 270: 1-20 (2014) - [j66]Mingge Deng, George E. Karniadakis:
Coarse-Grained Modeling of Protein Unfolding Dynamics. Multiscale Model. Simul. 12(1): 109-118 (2014) - [j65]Changho Kim, George E. Karniadakis:
Time Correlation Functions of Brownian Motion and Evaluation of Friction Coefficient in the Near-Brownian-Limit Regime. Multiscale Model. Simul. 12(1): 225-248 (2014) - [j64]Mohsen Zayernouri, George E. Karniadakis:
Fractional Spectral Collocation Method. SIAM J. Sci. Comput. 36(1) (2014) - [j63]Mohsen Zayernouri, George E. Karniadakis:
Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations. SIAM J. Sci. Comput. 36(4) (2014) - [j62]Zhongqiang Zhang, Michael V. Tretyakov, Boris Rozovskii, George E. Karniadakis:
A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise. SIAM J. Sci. Comput. 36(4) (2014) - [j61]Mohsen Zayernouri, Wanrong Cao, Zhongqiang Zhang, George E. Karniadakis:
Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations. SIAM J. Sci. Comput. 36(6) (2014) - [c20]Zheng Zhang, Xiu Yang, Giovanni Marucci, Paolo Maffezzoni, Ibrahim Abe M. Elfadel, George E. Karniadakis, Luca Daniel:
Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques. CICC 2014: 1-8 - [i4]Zheng Zhang, Xiu Yang, Ivan V. Oseledets, George E. Karniadakis, Luca Daniel:
Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition. CoRR abs/1407.3023 (2014) - [i3]Zheng Zhang, Xiu Yang, Giovanni Marucci, Paolo Maffezzoni, Ibrahim M. Elfadel, George E. Karniadakis, Luca Daniel:
Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques. CoRR abs/1409.4822 (2014) - [i2]Yu-Hang Tang, Shuhei Kudo, Xin Bian, Zhen Li, George E. Karniadakis:
Multiscale Universal Interface: A Concurrent Framework for Coupling Heterogeneous Solvers. CoRR abs/1411.1293 (2014) - 2013
- [j60]Zhongqiang Zhang, Xiu Yang, Guang Lin, George E. Karniadakis:
Numerical solution of the Stratonovich- and Ito-Euler equations: Application to the stochastic piston problem. J. Comput. Phys. 236: 15-27 (2013) - [j59]Daniele Venturi, Daniel M. Tartakovsky, Alexandre M. Tartakovsky, George E. Karniadakis:
Exact PDF equations and closure approximations for advective-reactive transport. J. Comput. Phys. 243: 323-343 (2013) - [j58]Ching-Long Lin, Grace C. Y. Peng, George E. Karniadakis:
Preface. J. Comput. Phys. 244: 1-3 (2013) - [j57]Leopold Grinberg, Dmitry A. Fedosov, George E. Karniadakis:
Parallel multiscale simulations of a brain aneurysm. J. Comput. Phys. 244: 131-147 (2013) - [j56]Minseok Choi, Themistoklis P. Sapsis, George E. Karniadakis:
A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes. J. Comput. Phys. 245: 281-301 (2013) - [j55]Yue Yu, Hyoungsu Baek, George E. Karniadakis:
Generalized fictitious methods for fluid-structure interactions: Analysis and simulations. J. Comput. Phys. 245: 317-346 (2013) - [j54]Xiu Yang, George E. Karniadakis:
Reweighted ℓ1ℓ1 minimization method for stochastic elliptic differential equations. J. Comput. Phys. 248: 87-108 (2013) - [j53]Mohsen Zayernouri, George E. Karniadakis:
Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation. J. Comput. Phys. 252: 495-517 (2013) - [j52]Heyrim Cho, Daniele Venturi, George E. Karniadakis:
Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations. SIAM J. Sci. Comput. 35(4) (2013) - [i1]Yu-Hang Tang, George E. Karniadakis:
Accelerating Dissipative Particle Dynamics Simulations on GPUs: Algorithms, Numerics and Applications. CoRR abs/1311.0402 (2013) - 2012
- [j51]Leopold Grinberg, Joseph A. Insley, Dmitry A. Fedosov, Vitali A. Morozov, Michael E. Papka, George E. Karniadakis:
Tightly Coupled Atomistic-Continuum Simulations of Brain Blood Flow on Petaflop Supercomputers. Comput. Sci. Eng. 14(6): 58-67 (2012) - [j50]Hyoungsu Baek, George E. Karniadakis:
A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. J. Comput. Phys. 231(2): 629-652 (2012) - [j49]Xiu Yang, Minseok Choi, Guang Lin, George E. Karniadakis:
Adaptive ANOVA decomposition of stochastic incompressible and compressible flows. J. Comput. Phys. 231(4): 1587-1614 (2012) - [j48]B. Yildirim, George E. Karniadakis:
A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation. J. Comput. Phys. 231(14): 4921-4953 (2012) - [j47]Daniele Venturi, George E. Karniadakis:
New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs. J. Comput. Phys. 231(21): 7450-7474 (2012) - [j46]Zhongqiang Zhang, Minseok Choi, George E. Karniadakis:
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions. SIAM J. Sci. Comput. 34(2) (2012) - [j45]Zhongqiang Zhang, Boris Rozovskii, Michael V. Tretyakov, George E. Karniadakis:
A Multistage Wiener Chaos Expansion Method for Stochastic Advection-Diffusion-Reaction Equations. SIAM J. Sci. Comput. 34(2) (2012) - [c19]Leopold Grinberg, Mingge Deng, Huan Lei, Joseph A. Insley, George Em Karniadakis:
Multiscale simulations of blood-flow: from a platelet to an artery. XSEDE 2012: 33:1-33:7 - 2011
- [j44]Huan Lei, Dmitry A. Fedosov, George E. Karniadakis:
Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics. J. Comput. Phys. 230(10): 3765-3779 (2011) - [j43]Hyoungsu Baek, George E. Karniadakis:
Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations. J. Comput. Phys. 230(12): 4384-4402 (2011) - [j42]Dmitry A. Fedosov, Huan Lei, Bruce Caswell, Subra Suresh, George E. Karniadakis:
Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria. PLoS Comput. Biol. 7(12) (2011) - [c18]Leopold Grinberg, Joseph A. Insley, Vitali A. Morozov, Michael E. Papka, George E. Karniadakis, Dmitry A. Fedosov, Kalyan Kumaran:
A new computational paradigm in multiscale simulations: application to brain blood flow. SC 2011: 5:1-5:5 - [c17]Joseph A. Insley, Leopold Grinberg, Michael E. Papka, George E. Karniadakis:
Electronic poster: visualizing multiscale simulation data. SC Companion 2011: 101-102 - [c16]Joseph A. Insley, Leopold Grinberg, Dmitry A. Fedosov, Vitali A. Morozov, Bruce Caswell, Michael E. Papka, George E. Karniadakis:
Blood flow: multi-scale modeling and visualization. SC Companion 2011: 139-140 - 2010
- [j41]Jasmine Foo, George E. Karniadakis:
Multi-element probabilistic collocation method in high dimensions. J. Comput. Phys. 229(5): 1536-1557 (2010) - [j40]Xian Luo, Ali Beskok, George E. Karniadakis:
Modeling electrokinetic flows by the smoothed profile method. J. Comput. Phys. 229(10): 3828-3847 (2010) - [j39]Leopold Grinberg, George E. Karniadakis:
A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows. J. Comput. Phys. 229(15): 5541-5563 (2010) - [j38]Marc I. Gerritsma, Jan-Bart van der Steen, Peter Vos, George E. Karniadakis:
Time-dependent generalized polynomial chaos. J. Comput. Phys. 229(22): 8333-8363 (2010) - [j37]P. Prempraneerach, Franz S. Hover, Michael S. Triantafyllou, George E. Karniadakis:
Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods. Reliab. Eng. Syst. Saf. 95(6): 632-646 (2010)
2000 – 2009
- 2009
- [j36]Dmitry A. Fedosov, George E. Karniadakis:
Triple-decker: Interfacing atomistic-mesoscopic-continuum flow regimes. J. Comput. Phys. 228(4): 1157-1171 (2009) - [j35]Xian Luo, Martin R. Maxey, George E. Karniadakis:
Smoothed profile method for particulate flows: Error analysis and simulations. J. Comput. Phys. 228(5): 1750-1769 (2009) - [j34]D. Liu, Eric E. Keaveny, Martin R. Maxey, George E. Karniadakis:
Force-coupling method for flows with ellipsoidal particles. J. Comput. Phys. 228(10): 3559-3581 (2009) - [j33]Leopold Grinberg, Dmitry Pekurovsky, Spencer J. Sherwin, George E. Karniadakis:
Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements. Parallel Comput. 35(5): 284-304 (2009) - 2008
- [j32]Dmitry A. Fedosov, Igor Pivkin, George E. Karniadakis:
Velocity limit in DPD simulations of wall-bounded flows. J. Comput. Phys. 227(4): 2540-2559 (2008) - [j31]Jasmine Foo, Xiaoliang Wan, George E. Karniadakis:
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications. J. Comput. Phys. 227(22): 9572-9595 (2008) - 2007
- [j30]Bruce M. Boghosian, Peter V. Coveney, Suchuan Dong, Lucas Finn, Shantenu Jha, George E. Karniadakis, Nicholas T. Karonis:
NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications. Clust. Comput. 10(3): 351-364 (2007) - [j29]Guang Lin, Xiaoliang Wan, Chau-Hsing Su, George E. Karniadakis:
Stochastic Computational Fluid Mechanics. Comput. Sci. Eng. 9(2): 21-29 (2007) - [j28]Robert M. Kirby, Zohar Yosibash, George E. Karniadakis:
Towards stable coupling methods for high-order discretization of fluid-structure interaction: Algorithms and observations. J. Comput. Phys. 223(2): 489-518 (2007) - [j27]Alexander Yakhot, T. Anor, George E. Karniadakis:
A Reconstruction Method for Gappy and Noisy Arterial Flow Data. IEEE Trans. Medical Imaging 26(12): 1681-1697 (2007) - [j26]Joseph A. Insley, Michael E. Papka, Suchuan Dong, George E. Karniadakis, Nicholas T. Karonis:
Runtime Visualization of the Human Arterial Tree. IEEE Trans. Vis. Comput. Graph. 13(4): 810-821 (2007) - 2006
- [j25]Suchuan Dong, Joseph A. Insley, Nicholas T. Karonis, Michael E. Papka, Justin Binns, George E. Karniadakis:
Simulating and visualizing the human arterial system on the TeraGrid. Future Gener. Comput. Syst. 22(8): 1011-1017 (2006) - [j24]Hasan Gunes, Sirod Sirisup, George E. Karniadakis:
Gappy data: To Krig or not to Krig? J. Comput. Phys. 212(1): 358-382 (2006) - [j23]Guang Lin, Leopold Grinberg, George E. Karniadakis:
Numerical studies of the stochastic Korteweg-de Vries equation. J. Comput. Phys. 213(2): 676-703 (2006) - [j22]George E. Karniadakis, James Glimm:
Uncertainty quantification in simulation science. J. Comput. Phys. 217(1): 1-4 (2006) - [j21]Guang Lin, Chau-Hsing Su, George E. Karniadakis:
Predicting shock dynamics in the presence of uncertainties. J. Comput. Phys. 217(1): 260-276 (2006) - [j20]Vasileios Symeonidis, George E. Karniadakis:
A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications. J. Comput. Phys. 218(1): 82-101 (2006) - [j19]Xiaoliang Wan, George E. Karniadakis:
A sharp error estimate for the fast Gauss transform. J. Comput. Phys. 219(1): 7-12 (2006) - [j18]David I. Gottlieb, Jan S. Hesthaven, George E. Karniadakis, Chi-Wang Shu:
Foreword. J. Sci. Comput. 27(1-3): 1-3 (2006) - [j17]Xiaoliang Wan, George E. Karniadakis:
Beyond Wiener-Askey Expansions: Handling Arbitrary PDFs. J. Sci. Comput. 27(1-3): 455-464 (2006) - [j16]Xiaoliang Wan, George E. Karniadakis:
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures. SIAM J. Sci. Comput. 28(3): 901-928 (2006) - [c15]Bruce M. Boghosian, Peter V. Coveney, Suchuan Dong, Lucas Finn, Shantenu Jha, George E. Karniadakis, Nicholas T. Karonis:
NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications. CLADE 2006: 34-42 - [c14]Peter Richardson, Igor Pivkin, George E. Karniadakis, David H. Laidlaw:
Blood Flow at Arterial Branches: Complexities to Resolve for the Angioplasty Suite. International Conference on Computational Science (3) 2006: 538-545 - [c13]Suchuan Dong, Nicholas T. Karonis, George E. Karniadakis:
Grid solutions for biological and physical cross-site simulations on the TeraGrid. IPDPS 2006 - [c12]Leopold Grinberg, Suchuan Dong, James Noble, Alexander Yakhot, George E. Karniadakis, Nicholas T. Karonis:
Poster reception - Human arterial tree simulation on TeraGrid. SC 2006: 152 - 2005
- [j15]Vasileios Symeonidis, George E. Karniadakis, Bruce Caswell:
A seamless approach to multiscale complex fluid simulation. Comput. Sci. Eng. 7(3): 39-46 (2005) - [j14]Suchuan Dong, George E. Karniadakis, Nicholas T. Karonis:
Cross-site computations on the TeraGrid. Comput. Sci. Eng. 7(5): 14-23 (2005) - [j13]Robert M. Kirby, George E. Karniadakis:
Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems. J. Sci. Comput. 22(1): 385-411 (2005) - [j12]Dongbin Xiu, Spencer J. Sherwin, Suchuan Dong, George E. Karniadakis:
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows. J. Sci. Comput. 25(1-2): 323-346 (2005) - [c11]Igor Pivkin, Eduardo Hueso, Rachel Weinstein, David H. Laidlaw, Sharon Swartz, George E. Karniadakis:
Simulation and Visualization of Air Flow Around Bat Wings During Flight. International Conference on Computational Science (2) 2005: 689-694 - 2004
- [j11]Jason S. Sobel, Andrew S. Forsberg, David H. Laidlaw, Robert C. Zeleznik, Daniel F. Keefe, Igor Pivkin, George E. Karniadakis, Peter Richardson, Sharon Swartz:
Particle Flurries: Synoptic 3D Pulsatile Flow Visualization. IEEE Computer Graphics and Applications 24(2): 76-85 (2004) - [j10]Suchuan Dong, George E. Karniadakis:
Multilevel Parallelization Models in CFD. J. Aerosp. Comput. Inf. Commun. 1(6): 256-268 (2004) - [j9]Suchuan Dong, George E. Karniadakis:
Dual-level parallelism for high-order CFD methods. Parallel Comput. 30(1): 1-20 (2004) - [j8]Xiaoliang Wan, Dongbin Xiu, George E. Karniadakis:
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. SIAM J. Sci. Comput. 26(2): 578-590 (2004) - [j7]Didier Lucor, George E. Karniadakis:
Adaptive Generalized Polynomial Chaos for Nonlinear Random Oscillators. SIAM J. Sci. Comput. 26(2): 720-735 (2004) - [c10]Didier Lucor, Chau-Hsing Su, George E. Karniadakis:
Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes. International Conference on Computational Science 2004: 827-834 - [c9]Rachel Weinstein, Eduardo Hueso, Igor Pivkin, Sharon Swartz, David H. Laidlaw, George E. Karniadakis, Kenneth Breuer:
Simulation and visualization of flow around bat wings during flight. SIGGRAPH Posters 2004: 103 - [c8]Igor Pivkin, Nicholas C. Yang, Peter Richardson, George E. Karniadakis, David H. Laidlaw:
Visualization of blood platelets in a virtual environment. SIGGRAPH Posters 2004: 111 - [c7]Eduardo Hueso, Igor Pivkin, Sharon Swartz, David H. Laidlaw, George E. Karniadakis, Kenny Breuer:
Visualization of Vortices in Simulated Airflow around Bat Wings During Flight. IEEE Visualization 2004: 20 - 2003
- [b1]George E. Karniadakis, Robert M. Kirby:
Parallel Scientific Computing in C++ and MPI - A Seamless Approach to Parallel Algorithms and their Implementation. Cambridge University Press 2003, ISBN 978-0-521-52080-5, pp. I-XI, 1-616 - [c6]Dongbin Xiu, Didier Lucor, Chau-Hsing Su, George E. Karniadakis:
Performance Evaluation of Generalized Polynomial Chaos. International Conference on Computational Science 2003: 346-354 - 2002
- [j6]M. Jardak, Chau-Hsing Su, George E. Karniadakis:
Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. J. Sci. Comput. 17(1-4): 319-338 (2002) - [j5]Jin Xu, Dongbin Xiu, George E. Karniadakis:
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. J. Sci. Comput. 17(1-4): 585-597 (2002) - [j4]Dongbin Xiu, George E. Karniadakis:
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM J. Sci. Comput. 24(2): 619-644 (2002) - [c5]Suchuan Dong, George E. Karniadakis:
Dual-level parallelism for deterministic and stochastic CFD problems. SC 2002: 42:1-42:17 - 2000
- [c4]Andrew S. Forsberg, David H. Laidlaw, Andries van Dam, Robert M. Kirby, George E. Karniadakis, Jonathan L. Elion:
Immersive virtual reality for visualizing flow through an artery. IEEE Visualization 2000: 457-460
1990 – 1999
- 1999
- [j3]Timothy C. Warburton, Spencer J. Sherwin, George E. Karniadakis:
Basis Functions for Triangular and Quadrilateral High-Order Elements. SIAM J. Sci. Comput. 20(5): 1671-1695 (1999) - [c3]George-Sosei Karamanos, Constantinos Evangelinos, Richard C. Boes, Robert M. Kirby, George E. Karniadakis:
Direct Numerical Simulation of Turbulence with a PC/Linux Cluster: Fact or Fiction? SC 1999: 53 - 1997
- [j2]Anil K. Bangia, Paul F. Batcho, Ioannis G. Kevrekidis, George E. Karniadakis:
Unsteady Two-Dimensional Flows in Complex Geometries: Comparative Bifurcation Studies with Global Eigenfunction Expansions. SIAM J. Sci. Comput. 18(3): 775-805 (1997) - [c2]Spencer J. Sherwin, Constantinos Evangelinos, H. Tufo, George Em Karniadakis:
hpDevelopment of a Parallel Unstructured Spectral/ Method for Unsteady Fluid Dynamics. Parallel CFD 1997: 273-280 - 1996
- [j1]Constantinos Evangelinos, George E. Karniadakis:
Parallel Cfd Benchmarks on Cray Computers. Parallel Algorithms Appl. 9(3-4): 273-298 (1996) - [c1]Constantinos Evangelinos, George E. Karniadakis:
Communication Performance Models in Prism : A Spectral Element-Fourier Parallel Navier-Stokes Solver. SC 1996: 20
Coauthor Index
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