George Em Karniadakis

98.5k total citations · 42 hit papers
686 papers, 64.1k citations indexed

About

George Em Karniadakis is a scholar working on Computational Mechanics, Statistical and Nonlinear Physics and Statistics, Probability and Uncertainty. According to data from OpenAlex, George Em Karniadakis has authored 686 papers receiving a total of 64.1k indexed citations (citations by other indexed papers that have themselves been cited), including 274 papers in Computational Mechanics, 209 papers in Statistical and Nonlinear Physics and 109 papers in Statistics, Probability and Uncertainty. Recurrent topics in George Em Karniadakis's work include Model Reduction and Neural Networks (181 papers), Fluid Dynamics and Turbulent Flows (133 papers) and Probabilistic and Robust Engineering Design (108 papers). George Em Karniadakis is often cited by papers focused on Model Reduction and Neural Networks (181 papers), Fluid Dynamics and Turbulent Flows (133 papers) and Probabilistic and Robust Engineering Design (108 papers). George Em Karniadakis collaborates with scholars based in United States, China and United Kingdom. George Em Karniadakis's co-authors include Paris Perdikaris, Maziar Raissi, Dongbin Xiu, Ameya D. Jagtap, Spencer J. Sherwin, Lu Lu, Liu Yang, Xuhui Meng, Sifan Wang and Bruce Caswell and has published in prestigious journals such as Science, Proceedings of the National Academy of Sciences and Physical Review Letters.

In The Last Decade

George Em Karniadakis

670 papers receiving 61.5k citations

Hit Papers

Physics-informed neural n... 1991 2026 2002 2014 2018 2021 2002 2020 2005 2.5k 5.0k 7.5k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
    2018 8.7k citations George Em Karniadakis et al. Journal of Computational Physics profile →
  2. Physics-informed machine learning
    2021 3.8k citations George Em Karniadakis et al. profile →
  3. The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
    2002 3.5k citations George Em Karniadakis et al. SIAM Journal on Scientific Computing profile →
  4. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
    2020 1.3k citations George Em Karniadakis et al. profile →
  5. Microflows and Nanoflows : Fundamentals and Simulation
    2005 1.2k citations George Em Karniadakis CERN Document Server (European Organization for Nuclear Research) profile →
  6. Modeling uncertainty in flow simulations via generalized polynomial chaos
    2003 1.1k citations George Em Karniadakis et al. Journal of Computational Physics profile →
  7. Spectral/hp Element Methods for Computational Fluid Dynamics
    2005 1.1k citations George Em Karniadakis et al. profile →
  8. High-order splitting methods for the incompressible Navier-Stokes equations
    1991 1.0k citations George Em Karniadakis, Steven A. Orszag et al. Journal of Computational Physics profile →
  9. Physics-informed neural networks (PINNs) for fluid mechanics: a review
    2021 1.0k citations George Em Karniadakis et al. profile →
  10. Hidden physics models: Machine learning of nonlinear partial differential equations
    2017 831 citations George Em Karniadakis et al. Journal of Computational Physics profile →
  11. Physics-informed neural networks for high-speed flows
    2019 782 citations Ameya D. Jagtap, George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  12. NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
    2020 744 citations George Em Karniadakis et al. Journal of Computational Physics profile →
  13. Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
    2020 693 citations Ameya D. Jagtap, George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  14. Physics-Informed Neural Networks for Heat Transfer Problems
    2021 686 citations George Em Karniadakis et al. profile →
  15. Spectral/hp Element Methods for CFD
    1999 680 citations George Em Karniadakis et al. profile →
  16. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
    2020 658 citations Xuhui Meng, George Em Karniadakis et al. Journal of Computational Physics profile →
  17. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
    2019 639 citations Ameya D. Jagtap, George Em Karniadakis et al. Journal of Computational Physics profile →
  18. Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
    2020 575 citations Ameya D. Jagtap, George Em Karniadakis Communications in Computational Physics profile →
  19. hp-VPINNs: Variational physics-informed neural networks with domain decomposition
    2020 467 citations George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  20. A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
    2019 420 citations Xuhui Meng, George Em Karniadakis Journal of Computational Physics profile →
  21. Discontinuous Galerkin Methods: Theory, Computation and Applications
    2011 415 citations Bernardo Cockburn, George Em Karniadakis et al. CERN Document Server (European Organization for Nuclear Research) profile →
  22. Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
    2019 405 citations George Em Karniadakis, Ellen Kuhl et al. profile →
  23. PPINN: Parareal physics-informed neural network for time-dependent PDEs
    2020 388 citations Xuhui Meng, Zhen Li et al. Computer Methods in Applied Mechanics and Engineering profile →
  24. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
    2022 388 citations Xuhui Meng, George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  25. Machine learning of linear differential equations using Gaussian processes
    2017 376 citations George Em Karniadakis et al. Journal of Computational Physics profile →
  26. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
    2019 318 citations George Em Karniadakis et al. Journal of Computational Physics profile →
  27. Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
    2017 279 citations George Em Karniadakis et al. profile →
  28. What is the fractional Laplacian? A comparative review with new results
    2019 255 citations Xiaoning Zheng, George Em Karniadakis et al. Journal of Computational Physics profile →
  29. A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
    2022 249 citations Somdatta Goswami, George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  30. Extraction of mechanical properties of materials through deep learning from instrumented indentation
    2020 242 citations George Em Karniadakis et al. Proceedings of the National Academy of Sciences profile →
  31. Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
    2021 234 citations George Em Karniadakis et al. profile →
  32. Physics‐Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions
    2022 234 citations George Em Karniadakis et al. profile →
  33. Fractional Sturm–Liouville eigen-problems: Theory and numerical approximation
    2013 228 citations George Em Karniadakis et al. Journal of Computational Physics profile →
  34. Analyses of internal structures and defects in materials using physics-informed neural networks
    2022 221 citations George Em Karniadakis et al. profile →
  35. Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
    2023 215 citations Xuhui Meng, Zongren Zou et al. Journal of Computational Physics profile →
  36. Physics-informed neural networks for inverse problems in supersonic flows
    2022 205 citations Ameya D. Jagtap, George Em Karniadakis et al. profile →
  37. Reinforcement learning for bluff body active flow control in experiments and simulations
    2020 175 citations George Em Karniadakis et al. Proceedings of the National Academy of Sciences profile →
  38. Tackling the curse of dimensionality with physics-informed neural networks
    2024 72 citations George Em Karniadakis et al. Neural Networks profile →
  39. Residual-based attention in physics-informed neural networks
    2024 68 citations Juan Diego Toscano, George Em Karniadakis et al. Computer Methods in Applied Mechanics and Engineering profile →
  40. From PINNs to PIKANs: recent advances in physics-informed machine learning
    2025 60 citations Juan Diego Toscano, Zongren Zou et al. profile →
  41. A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
    2024 58 citations Juan Diego Toscano, Zongren Zou et al. Computer Methods in Applied Mechanics and Engineering profile →
  42. Laplace neural operator for solving differential equations
    2024 52 citations Somdatta Goswami, George Em Karniadakis et al. profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
George Em Karniadakis United States 107 22.3k 21.9k 10.8k 7.1k 6.5k 686 64.1k
Saul A. Teukolsky United States 66 4.6k 0.2× 6.2k 0.3× 1.2k 0.1× 3.4k 0.5× 2.3k 0.4× 233 74.6k
Paris Perdikaris United States 37 4.5k 0.2× 10.6k 0.5× 2.2k 0.2× 2.5k 0.3× 1.0k 0.2× 79 20.4k
Stephen Boyd United States 99 16.9k 0.8× 3.3k 0.2× 2.2k 0.2× 7.4k 1.0× 517 0.1× 441 91.4k
Gene H. Golub United States 84 10.7k 0.5× 3.4k 0.2× 1.7k 0.2× 2.2k 0.3× 960 0.1× 294 45.6k
Stanley Osher United States 105 43.8k 2.0× 2.2k 0.1× 688 0.1× 5.7k 0.8× 1.4k 0.2× 457 81.2k
David L. Donoho United States 95 45.1k 2.0× 1.3k 0.1× 1.7k 0.2× 5.2k 0.7× 1.1k 0.2× 227 101.0k
Brian P. Flannery United States 33 3.5k 0.2× 4.2k 0.2× 937 0.1× 2.8k 0.4× 2.1k 0.3× 79 49.1k
Steven L. Brunton United States 53 5.8k 0.3× 8.8k 0.4× 2.5k 0.2× 2.9k 0.4× 741 0.1× 212 16.9k
William T. Vetterling United States 24 3.5k 0.2× 4.2k 0.2× 932 0.1× 2.8k 0.4× 1.9k 0.3× 62 47.5k
Jorge Nocedal United States 44 6.0k 0.3× 1.8k 0.1× 1.4k 0.1× 2.5k 0.3× 1.1k 0.2× 105 37.3k

Countries citing papers authored by George Em Karniadakis

Since Specialization
Citations

This map shows the geographic impact of George Em Karniadakis's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by George Em Karniadakis with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites George Em Karniadakis more than expected).

Fields of papers citing papers by George Em Karniadakis

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by George Em Karniadakis. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by George Em Karniadakis. The network helps show where George Em Karniadakis may publish in the future.

Co-authorship network of co-authors of George Em Karniadakis

This figure shows the co-authorship network connecting the top 25 collaborators of George Em Karniadakis. A scholar is included among the top collaborators of George Em Karniadakis based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with George Em Karniadakis. George Em Karniadakis is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Wu, Chenxi, et al.. (2025). Artificial to Spiking Neural Networks Conversion with Calibration in Scientific Machine Learning. SIAM Journal on Scientific Computing. 47(3). C559–C577.
2.
Karniadakis, George Em, et al.. (2024). SMS: Spiking marching scheme for efficient long time integration of differential equations. Journal of Computational Physics. 516. 113363–113363. 2 indexed citations
3.
Zhong, Ming, et al.. (2024). Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. Journal of Computational Physics. 505. 112917–112917. 13 indexed citations
4.
Toscano, Juan Diego, Chenxi Wu, Antonio Ladrón-de-Guevara, et al.. (2024). Inferring in vivo murine cerebrospinal fluid flow using artificial intelligence velocimetry with moving boundaries and uncertainty quantification. Interface Focus. 14(6). 20240030–20240030. 5 indexed citations
5.
Zeng, Fanhai, et al.. (2024). Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models. Communications in Computational Physics. 35(1). 1–37. 3 indexed citations
6.
Goswami, Somdatta, et al.. (2023). On the influence of over-parameterization in manifold based surrogates and deep neural operators. Journal of Computational Physics. 479. 112008–112008. 28 indexed citations
7.
Hao, Yue, Patricio Clark Di Leoni, Olaf Marxen, et al.. (2023). Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators. Journal of Computational Science. 73. 102120–102120. 14 indexed citations
8.
Xu, Mengjia, et al.. (2023). TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers. Neural Networks. 172. 106086–106086. 2 indexed citations
9.
Haghighat, Ehsan, Umair bin Waheed, & George Em Karniadakis. (2023). En-DeepONet: An enrichment approach for enhancing the expressivity of neural operators with applications to seismology. Computer Methods in Applied Mechanics and Engineering. 420. 116681–116681. 24 indexed citations
10.
Perego, Mauro, et al.. (2023). Multifidelity deep operator networks for data-driven and physics-informed problems. Journal of Computational Physics. 493. 112462–112462. 42 indexed citations
11.
Jagtap, Ameya D., et al.. (2023). A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions. Journal of Computational Physics. 493. 112464–112464. 34 indexed citations
12.
Linka, Kevin, Amelie Schäfer, Xuhui Meng, et al.. (2022). Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems. Computer Methods in Applied Mechanics and Engineering. 402. 115346–115346. 104 indexed citations
13.
Jagtap, Ameya D. & George Em Karniadakis. (2021). Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations.. National Conference on Artificial Intelligence. 1 indexed citations
14.
Sampani, Konstantina, He Li, Xiaoning Zheng, et al.. (2020). Computational fluid dynamics (CFD) estimation of thrombus formation in diabetic retinal microaneurysms (MAs). Investigative Ophthalmology & Visual Science. 61(7). 5023–5023. 1 indexed citations
15.
Li, Zhen, Xin Bian, Xiantao Li, & George Em Karniadakis. (2015). Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism. The Journal of Chemical Physics. 143(24). 243128–243128. 97 indexed citations
16.
Lei, Huan & George Em Karniadakis. (2013). Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations. Proceedings of the National Academy of Sciences. 110(28). 11326–11330. 59 indexed citations
17.
Cockburn, Bernardo, George Em Karniadakis, & Chi‐Wang Shu. (2011). Discontinuous Galerkin Methods: Theory, Computation and Applications. CERN Document Server (European Organization for Nuclear Research). 415 indexed citations breakdown →
18.
Baek, Hyoungsu, Mahesh Jayaraman, & George Em Karniadakis. (2007). Distribution of WSS on the Internal Carotid Artery with an Aneurysm. Bulletin of the American Physical Society. 60.
19.
Grinberg, Lea T., Alexander Yakhot, & George Em Karniadakis. (2006). DNS of flow in stenosed carotid artery. Bulletin of the American Physical Society. 59(28). 3405–8. 1 indexed citations
20.
Tomboulides, Ananias, Steven A. Orszag, & George Em Karniadakis. (1991). THREE-DIMENSIONAL SIMULATION OF FLOW PAST A SPHERE. 1 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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