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The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE).
The Kuramoto-Sivashinsky equation: a bridge between pde’s and dynamical systems
J. M. Hyman and B. Nicolaenko · 1986
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Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Multilayer feedforward networks are universal approximators
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Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
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Remark on the pressure boundary condition for the projection method
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Universal approximation bounds for superpositions of a sigmoidal function
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Navier-Stokes equations: theory and numerical analysis , volume 343
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Linear and nonlinear instability waves in spatially developing two-phase mixing layers
L. C. Cheung and T. A. Zaki · 2010
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A nonlinear pse method for two-fluid shear flows with complex interfacial topology
L. C. Cheung and T. A. Zaki · 2011
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Z. Mao, L. Lu, O. Marxen, T. A. Zaki, and G. E. Karniadakis · 2011
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Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow
G. J. Chandler and R. R. Kerswell · 2013
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Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
D. Lucas and R. R. Kerswell · 2015
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Sensitivity of high-speed boundary-layer stability to base-flow distortion
J. Park and T. A. Zaki · 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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S. Cai, Z. Wang, L. Lu, T. A. Zaki, and G. E. Karniadakis · 2020
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Fourier neural operator for parametric partial differential equations
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2020
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A unified deep artificial neural network approach to partial differential equations in complex geometries
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L. Lu, P. Jin, and G. E. Karniadakis · 2019
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J. Lu, Z. Shen, H. Yang, and S. Zhang · 2020
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Two-layer neural networks for partial differential equations: Optimization and generalization theory
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Revealing the state space of turbulence using machine learning
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Understanding and mitigating gradient pathologies in physics-informed neural networks
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Systems biology informed deep learning for inferring parameters and hidden dynamics
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