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We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations.
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On the camassa-holm equation and a direct method of solution i. bilinear form and solitary waves
A. Parker · 2004
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Model reduction and neural networks for parametric PDEs, 2020
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2005
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On the camassa–holm equation and a direct method of solution. ii. soliton solutions
A. Parker · 2005
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On the camassa–holm equation and a direct method of solution. iii. n-soliton solutions
A. Parker · 2005
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Convergence of a finite difference scheme for the camassa–holm equation
H. Holden and X. Raynaud · 2006
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The korteweg–de vries–kawahara equation in a bounded domain and some numerical results
J. C. Ceballos, M. Sepúlveda, and O. P. Vera Villagrán · 2007
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Global well-posedness in l 2 l^{2} for the periodic benjamin–ono equation
L. Molinet · 2008
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A. Faminskii and N. Larkin · 2010
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Error estimate for a fully discrete spectral scheme for korteweg-de vries-kawahara equation
U. Koley · 2012
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Practical methods of optimization
R. Fletcher · 2013
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The water waves problem: Mathematical analysis and asymptotics
D. Lannes · 2013
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Convergence of finite difference schemes for the benjamin–ono equation
R. Dutta, H. Holden, U. Koley, and N. H. Risebro · 2015
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Convergence of a higher order scheme for the korteweg–de vries equation
R. Dutta, U. Koley, and N. H. Risebro · 2015
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Convergence of a fully discrete finite difference scheme for the korteweg-de vries equation
H. Holden, U. Koley, and H. Risebro · 2015
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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Deep learning
I. Goodfellow, Y. Benigo, and A. Courville · 2016
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Finite difference schemes for the korteweg–de vries–kawahara equation
U. Koley · 2016
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fpinns: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
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Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
A. D. Jagtap and G. E. Karniadakis · 2020
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
A. D. Jagtap, E. Kharazmi, and G. E. Karniadakis · 2020
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Fourier neural operator for parametric partial differential equations
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
W. E, J. Han, and A. Jentzen · 2017
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Automatic differentiation in pytorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
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Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
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Hidden physics models: Machine learning of nonlinear partial differential equations
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M. Raissi, A. Yazdani, and G. E. Karniadakis · 2018
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Y. Chen, L. Lu, G. E. Karniadakis, and L. D. Negro · 2019
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Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2020
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Y. Liu, X. Meng, and G. E. Karniadakis · 2020
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K. . O. Lye, S. Mishra, P. Chandrasekhar, and D. Ray · 2020
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A multi-level procedure for enhancing accuracy of machine learning algorithms
K. O. LYE, S. MISHRA, and R. MOLINARO · 2020
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Deep learning observables in computational fluid dynamics
K. O. Lye, S. Mishra, and D. Ray · 2020
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Physics-informed neural networks for high-speed flows
Z. Mao, A. D. Jagtap, and G. E. Karniadakis · 2020
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S. Mishra and R. Molinaro · 2020
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S. Mishra and R. Molinaro · 2020
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Physics informed neural networks for simulating radiative transfer
S. Mishra and R. Molinaro · 2020
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Numerical solution for the kawahara equation using local rbf-fd meshless method
M. N. Rasoulizadeh and J. Rashidinia · 2020
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On the convergence and generalization of physics informed neural networks
Y. Shin, J. Darbon, and G. E. Karniadakis · 2020
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K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, and G. E. Karniadakis · 2020
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Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
T. DeRyck and S. Mishra · 2021
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Error estimates for deeponets: A deep learning framework in infinite dimensions
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