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Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP.
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N. Tishby, F. C. Pereira, W. Bialek, The information bottleneck method, arXiv preprint physics/0004057 (2000)
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D. A. Sprecher, S. Draghici, Space-filling curves and Kolmogorov superposition-based neural networks, Neural Networks 15 (1) (2002) 57–67
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M. Köppen, On the training of a Kolmogorov network, in: Artificial Neural Networks—ICANN 2002: International Conference Madrid, Spain, August 28–30, 2002 Proceedings 12, Springer, 2002, pp. 474–479
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J.-L. Guermond, R. Pasquetti, B. Popov, Entropy viscosity method for nonlinear conservation law, Journal of Computational Physics 230 (11) (2011) 4248–4267
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P.-E. Leni, Y. D. Fougerolle, F. Truchetet, The kolmogorov spline network for image processing, in: Image Processing: Concepts, Methodologies, Tools, and Applications, IGI Global, 2013, pp. 54–78
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N. Tishby, N. Zaslavsky, Deep learning and the information bottleneck principle, in: 2015 ieee information theory workshop (itw), IEEE, 2015, pp. 1–5
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K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp. 770–778
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A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, I. Polosukhin, Attention is all you need, Advances in neural information processing systems 30 (2017)
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H. Li, Z. Xu, G. Taylor, C. Studer, T. Goldstein, Visualizing the loss landscape of neural nets, Advances in neural information processing systems 31 (2018)
2018
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M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational physics 378 (2019) 686–707
2019
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N. Rahaman, A. Baratin, D. Arpit, F. Draxler, M. Lin, F. Hamprecht, Y. Bengio, A. Courville, On the spectral bias of neural networks, in: International conference on machine learning, PMLR, 2019, pp. 5301–5310
2019
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S. Greydanus, M. Dzamba, J. Yosinski, Hamiltonian neural networks, Advances in neural information processing systems 32 (2019)
2019
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A. Garg, S. S. Kagi, Hamiltonian neural networks (2019)
2019
Earlier work this paper cites.
Z. Wang, M. S. Triantafyllou, Y. Constantinides, G. Karniadakis, An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe, Journal of Fluid Mechanics 859 (2019) 691–730
2019
Earlier work this paper cites.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, Generative adversarial networks, Communications of the ACM 63 (11) (2020) 139–144
2020
Cited alongside, same era.
A. D. Jagtap, K. Kawaguchi, G. E. Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics 404 (2020) 109136
2020
Cited alongside, same era.
Z. Goldfeld, Y. Polyanskiy, The information bottleneck problem and its applications in machine learning, IEEE Journal on Selected Areas in Information Theory 1 (1) (2020) 19–38
2020
Cited alongside, same era.
Z. Mao, A. D. Jagtap, G. E. Karniadakis, Physics-informed neural networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering 360 (2020) 112789
2020
Cited alongside, same era.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
Y. He, Z. Wang, H. Xiang, X. Jiang, D. Tang, An artificial viscosity augmented physics-informed neural network for incompressible flow, Applied Mathematics and Mechanics 44 (7) (2023) 1101–1110
2023
Later among the works it cites.
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X. Meng, Z. Li, D. Zhang, G. E. Karniadakis, PPINN: Parareal physics-informed neural network for time-dependent PDEs, Computer Methods in Applied Mechanics and Engineering 370 (2020) 113250
2020
Cited alongside, same era.
2020
Cited alongside, same era.
K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, G. E. Karniadakis, Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks, Journal of Nondestructive Evaluation 39 (2020) 1–20
2020
Cited alongside, same era.
2021
Cited alongside, same era.
G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang, Physics-informed machine learning, Nature Reviews Physics 3 (6) (2021) 422–440
2021
Cited alongside, same era.
L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via deeponet based on the universal approximation theorem of operators, Nature machine intelligence 3 (3) (2021) 218–229
2021
Cited alongside, same era.
S. Cai, Z. Mao, Z. Wang, M. Yin, G. E. Karniadakis, Physics-informed neural networks (PINNs) for fluid mechanics: A review, Acta Mechanica Sinica 37 (12) (2021) 1727–1738
2021
Cited alongside, same era.
L. Yang, X. Meng, G. E. Karniadakis, B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Journal of Computational Physics 425 (2021) 109913
2021
Cited alongside, same era.
M. Yin, Z. Zou, E. Zhang, C. Cavinato, J. D. Humphrey, G. E. Karniadakis, A generative modeling framework for inferring families of biomechanical constitutive laws in data-sparse regimes, Journal of the Mechanics and Physics of Solids 181 (2023) 105424
2023
Later among the works it cites.
2023
Later among the works it cites.
2024
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2024
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Z. Bozorgasl, H. Chen, Wav-KAN: Wavelet Kolmogorov-Arnold Networks (2024) · 2024
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NLNR, Jacobikan, https://github.com/mintisan/awesome-kan/ (2024)
2024
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SynodicMonth, ChebyKAN, https://github.com/SynodicMonth/ChebyKAN/ (2024)
2024
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2024
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S. S. Bhattacharjee, TorchKAN: Simplified KAN Model with Variations, https://github.com/1ssb/torchkan/ (2024)
2024
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2024
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2024
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Z. Zou, X. Meng, G. E. Karniadakis, Correcting model misspecification in physics-informed neural networks (PINNs), Journal of Computational Physics 505 (2024) 112918
2024
Closest in time.
Z. Zhang, Z. Zou, E. Kuhl, G. E. Karniadakis, Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression, Computer Methods in Applied Mechanics and Engineering 419 (2024) 116647
2024
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P. Chen, T. Meng, Z. Zou, J. Darbon, G. E. Karniadakis, Leveraging multitime Hamilton–Jacobi PDEs for certain scientific machine learning problems, SIAM Journal on Scientific Computing 46 (2) (2024) C216–C248
2024
Closest in time.
S. J. Anagnostopoulos, J. D. Toscano, N. Stergiopulos, G. E. Karniadakis, Residual-based attention in physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering 421 (2024) 116805
2024
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2024
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K. Shukla, V. Oommen, A. Peyvan, M. Penwarden, N. Plewacki, L. Bravo, A. Ghoshal, R. M. Kirby, G. E. Karniadakis, Deep neural operators as accurate surrogates for shape optimization, Engineering Applications of Artificial Intelligence 129 (2024) 107615
2024
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Z. Zou, X. Meng, A. F. Psaros, G. E. Karniadakis, NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators, SIAM Review 66 (1) (2024) 161–190
2024
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J. Lin, awesome-kan, https://github.com/SpaceLearner/JacobiKAN/ (2024)
2024
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B. Ter-Avanesov, awesome-kan, https://github.com/Boris-73-TA/OrthogPolyKANs/ (2024)
2024
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