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George Em Karniadakis

Brown University

Box 1860

Providence, RI 02912

United States

SCHOLARLY PAPERS

30

DOWNLOADS

2,343

TOTAL CITATIONS
Rank 22,711

SSRN RANKINGS

Top 22,711

in Total Papers Citations

84

Scholarly Papers (30)

1.

Deepomamba: State-Space Model for Spatio-Temporal Pde Neural Operator Learning

Number of pages: 29 Posted: 22 Feb 2025
Zheyuan Hu, Qianying Cao, Kenji Kawaguchi and George Em Karniadakis
National University of Singapore (NUS), Brown University, National University of Singapore (NUS) and Brown University
Downloads 380 (194,151)

Abstract:

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Neural Operator, State-Space Model, Mamba, Spatio-Temporal PDE

2.

Multi-Head Physics-Informed Neural Networks for Learning Functional Priors and Uncertainty Quantification

Number of pages: 30 Posted: 18 Nov 2024
Zongren Zou and George Em Karniadakis
Brown University and Brown University
Downloads 264 (288,370)
Citation 27

Abstract:

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Sparse and noisy data, PINNs, functional priors, uncertainty quantification, normalizing flows, Bayesian inference

3.

Accelerating Gradient Descent and Adam Via Fractional Gradients

Number of pages: 28 Posted: 08 Jul 2022
Yeonjong Shin, Jérôme Darbon and George Em Karniadakis
Korea Advanced Institute of Science and Technology (KAIST) - Korea Advanced Institute of Science and Technology (KAIST), Students, Brown University and Brown University
Downloads 177 (428,796)

Abstract:

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Caputo fractional derivative, Non-local calculus, optimization, Adam, Neural Networks

4.

Residual-Based Attention in Pinns

Number of pages: 35 Posted: 28 Sep 2023
École Polytechnique Fédérale de Lausanne (EPFL), Brown University, affiliation not provided to SSRN and Brown University
Downloads 173 (435,504)

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Residual-based attention, PINNs accuracy, adaptive weights.

5.

Ultra-Fast Meta-Solvers for 3d Scattering Problems Using Neural Operators Trained as Foundation Models

Number of pages: 22 Posted: 13 Dec 2024
Korea Advanced Institute of Science and Technology (KAIST), Brown University, Brown University, Tel Aviv University - Department of applied Mathematics, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 155 (480,208)

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Scientific Machine Learning, wave scattering, Helmholtz equation, neural operator, Krylov methods, DeepONet

6.

Which Optimizer Works Best for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks?

Number of pages: 41 Posted: 20 May 2025
Brown University, Brown University, affiliation not provided to SSRN, Brown University and Brown University
Downloads 144 (511,933)
Citation 16

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Quasi-Newton Methods, Second-Order Optimization, Kolmogorov-Arnold Networks (PIKANs), Physics-Informed Neural Networks (PINNs)

7.

Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures

Number of pages: 24 Posted: 14 Dec 2024
Brown University, affiliation not provided to SSRN, Brown University, ETH Zürich and Brown University
Downloads 119 (600,462)

Abstract:

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Operator neural networks, Phase-field approach, Physics-informed methodologies, Data-driven modeling, Crack propagation, Kolmogorov-Arnold Network (KAN)

8.

Large Scale Scattering Using Fast Solvers Based on Neural Operators

Number of pages: 28 Posted: 21 May 2024
Brown University, Brown University, Brown University, Tel Aviv University - Department of applied Mathematics, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 86 (765,566)
Citation 1

Abstract:

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Scientific machine learning, wave scattering, Helmholtz equation, neural operator, DeepONet

9.

A Comprehensive and Fair Comparison between Mlp and Kan Representations for Differential Equations and Operator Networks

Number of pages: 38 Posted: 08 Jun 2024
Brown University, Brown University, Brown University, Brown University and Brown University
Downloads 78 (816,709)
Citation 11

Abstract:

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Scientific machine learning, Kolmogorov-Arnold networks, Physics-informed neural networks, operator networks, partial differential equations

10.

Correcting Model Misspecification in Physics-Informed Neural Networks (Pinns)

Number of pages: 28 Posted: 30 Oct 2023
Zongren Zou, Xuhui Meng and George Em Karniadakis
Brown University, Huazhong University of Science and Technology and Brown University
Downloads 72 (860,052)

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model uncertainty, Physics-Informed Neural Networks, model misspecification, Uncertainty Quantification, non-Newtonian flows, symbolic regression

11.

A Unified Scalable Framework for Causal Sweeping Strategies for Physics-Informed Neural Networks (Pinns) and Their Temporal Decompositions

Number of pages: 33 Posted: 14 Mar 2023
University of Utah - School of Computing and Scientific Computing and Imaging Institute, Brown University, University of Utah - School of Computing, Brown University and University of Utah - School of Computing and Scientific Computing and Imaging Institute
Downloads 72 (860,052)

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Physics-Informed Neural Networks (PINNs), causality, domain decomposition, transfer learning

12.

Learning Stiff Chemical Kinetics Using Extended Deep Neural Operators

Number of pages: 25 Posted: 19 Aug 2023
Brown University, Brown University, University of Pittsburgh, affiliation not provided to SSRN and Brown University
Downloads 70 (875,328)

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Stiff problems, Scientific machine learning, Neural operators, Combustion

13.

Sympgnns: Symplectic Graph Neural Networks for Identifying High-Dimensional Hamiltonian Systems and Node Classification

Number of pages: 17 Posted: 18 Sep 2024
Alan John Varghese, Zhen Zhang and George Em Karniadakis
Brown University, Brown University and Brown University
Downloads 66 (907,769)
Citation 1

Abstract:

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deep learning, Graph neural networks, Physics-informed, Hamiltonian systems, Symplectic maps, node classification

14.

Reliable Extrapolation of Deep Neural Operators Informed by Physics or Sparse Observations

Number of pages: 44 Posted: 02 Mar 2023
Min Zhu, Handi Zhang, Anran Jiao, George Em Karniadakis and Lu Lu
University of Pennsylvania, University of Pennsylvania, University of Pennsylvania, Brown University and University of Pennsylvania
Downloads 58 (980,173)

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Neural operators, DeepONet, Extrapolation complexity, Fine-tuning, Multifidelity learning, Out-of-distribution inference

15.

State-Space Models are Accurate and Efficient Neural Operators for Dynamical Systems

Number of pages: 35 Posted: 17 Oct 2024
National University of Singapore (NUS), Brown University, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 57 (989,921)

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Neural Operator, State-Space Model, Mamba, dynamical system

16.

Tackling the Curse of Dimensionality with Physics-Informed Neural Networks

Number of pages: 35 Posted: 07 Dec 2023
Zheyuan Hu, Khemraj Shukla, George Em Karniadakis and Kenji Kawaguchi
National University of Singapore (NUS), Brown University, Brown University and National University of Singapore (NUS)
Downloads 47 (1,097,529)
Citation 6

Abstract:

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Physics-Informed Neural Networks, Curse of Dimensionality

17.

Uncertainty Quantification for Noisy Inputs-Outputs in Physics-Informed Neural Networks and Neural Operators

Number of pages: 28 Posted: 07 May 2024
Zongren Zou, Xuhui Meng and George Em Karniadakis
Brown University, Huazhong University of Science and Technology and Brown University
Downloads 43 (1,145,425)
Citation 6

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uncertainty quantification, Bayesian inference, noisy inputs-outputs, PINNs, neural operators, synergistic learning

18.

Automatic Discovery of Optimal Meta-Solvers Via Multi-Objective Optimization

Number of pages: 35 Posted: 04 Feb 2025
Youngkyu Lee, Shanqing Liu, Jérôme Darbon and George Em Karniadakis
Korea Advanced Institute of Science and Technology (KAIST), Brown University, Brown University and Brown University
Downloads 42 (1,157,785)
Citation 1

Abstract:

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operator learning, Preconditioning, Hybridization, Spectral bias, Numerical optimization, Pareto optimality

19.

Crack Path Prediction with Operator Learning Using Discrete Particle System Data Generation

Number of pages: 21 Posted: 07 Aug 2025
Brown University, Clemson University, Brown University, affiliation not provided to SSRN, Clemson University and Brown University
Downloads 41 (1,170,409)

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Crack PropagationDiscrete Particle SystemsDeep Operator Networks (DeepONets)Constitutively Informed Particle Dynamics (CPD)Fracture PredictionFusion DeepONet

20.

Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet–Transolver Framework

Number of pages: 18 Posted: 17 Sep 2025
Varun Kumar, Jing Bi, Cyril Ngo Ngoc, Victor Oancea and George Em Karniadakis
Brown University, affiliation not provided to SSRN, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 30 (1,332,057)

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PET bottle buckling, Transolver, DeepONet, computational mechanics, scientific machine learning

21.

Red Blood Cell Passage Through Deformable Interendothelial Slits in the Spleen: Insights into Splenic Filtration and Hemodynamics

Number of pages: 27 Posted: 03 Apr 2024
Brown University, University of Georgia, Université Paris Cité, Université Paris Cité, Zhejiang University, Western University, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 27 (1,359,097)

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Deformable interendothelial slits spleen Filtration Dissipartive particle dynamics SSickle cell disease

22.

Transformerg2g: Adaptive Time-Stepping for Learning Temporal Graph Embeddings Using Transformers

Number of pages: 16 Posted: 24 Jul 2023
Alan John Varghese, Aniruddha Bora, Mengjia Xu and George Em Karniadakis
Brown University, Brown University, Brown University and Brown University
Downloads 21 (1,436,435)
Citation 1

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Graph Embedding, Transformer, dynamic graphs, Link prediction, unsupervised contrastive learning, long-term dependencies

23.

A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes

Number of pages: 30 Posted: 23 May 2023
Brown University, Brown University, Brown University, Yale University, Yale University and Brown University
Downloads 21 (1,436,435)

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Constitutive Relation, Uncertainty Quantification, Functional Prior, Generative Adversarial Network, Deep Operator Network, Bayesian Inference

24.

Inception UNet (IUNet) and Multi-scale Multi-branch (M&M) UNet Plug-In Neural Operators for Online Bias Correction in E3SM

Number of pages: 41 Posted: 09 Feb 2026
Brown University, Government of the United States of America - Pacific Northwest National Laboratory, Brown University, Government of the United States of America - Pacific Northwest National Laboratory, Brown University and Government of the United States of America - Pacific Northwest National Laboratory
Downloads 20 (1,459,862)

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Neural Operator, UNet, Inception UNet (IUNet), Multi-scale Multi-branch (M&M), Earth System Modeling, Bias Correction

25.

Bridging Scales in Multiscale Bubble Growth Dynamics with Correlated Fluctuations Using Neural Operator Learning

Number of pages: 14 Posted: 22 Mar 2024
Minglei Lu, Chensen Lin, Martian Maxey, George Em Karniadakis and Zhen Li
Clemson University, Fudan University, Brown University, Brown University and Clemson University
Downloads 20 (1,448,301)
Citation 6

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Multiscale Modeling, multiphase flow, Deep Learning, Dissipative Particle Dynamics, Rayleigh-Plesset Equation

26.

GIMLET: Generalizable and InterpretableModel Learning through Embedded Thermodynamics

Number of pages: 26 Posted: 10 Feb 2026
Suguru Shiratori:, Elham kiyani, Khemraj Shukla and George Em Karniadakis
Tokyo City University, Brown University, Brown University and Brown University
Downloads 18 (1,491,251)

Abstract:

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structure-preserving, physics-informed neural networks, Gray-box discovery, Functional derivatives, Non-equilibrium thermodynamics

27.

Neurosem: A Hybrid Framework for Simulating Multiphysics Problems by Coupling Pinns and Spectral Elements

Number of pages: 33 Posted: 31 Jul 2024
Brown University, Brown University, affiliation not provided to SSRN, Brown University, Brown University and Brown University
Downloads 16 (1,491,251)
Citation 4

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physics-informed machine learning, PINNs, spectral element method, data assimilation, multiphysics problems, heat transfer

28.

Tackling the Curse of Dimensionality in Fractional and Tempered Fractional Pdes with Physics-Informed Neural Networks

Number of pages: 16 Posted: 19 Jun 2024
Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang and George Em Karniadakis
National University of Singapore (NUS), affiliation not provided to SSRN, Worcester Polytechnic Institute and Brown University
Downloads 14 (1,509,872)
Citation 4

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Physics-informed neural networks, Curse of Dimensionality, Fractional and Tempered Fractional PDEs, High-Dimensional PDEs

29.

Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles

Number of pages: 36 Posted: 11 May 2026
Brown University, affiliation not provided to SSRN, affiliation not provided to SSRN, affiliation not provided to SSRN and Brown University
Downloads 10 (1,541,665)

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30.

Clot Treatment Via Spinning-Induced Fibrin Microstructure Densification and Clot Volume Reduction

Number of pages: 16
Yilong Chang, guansheng li, Jay Sim, George Em Karniadakis and Ruike Renee Zhao
Stanford University, Brown University, Stanford University, Brown University and Stanford University
Downloads 2

Abstract:

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Milli-spinner, Blood clot, Clot debulking, Fibrin densification, Clot volume reduction