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Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing.
On the solution of nonlinear hyperbolic differential equations by finite differences
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Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
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Uncertainty quantification in computational fluid dynamics , volume 92
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Data-driven discovery of partial differential equations
A machine learning framework for data driven acceleration of computations of differential equations
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Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
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Multistep neural networks for data-driven discovery of nonlinear dynamical systems
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Deep fluids: A generative network for parameterized fluid simulations
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Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
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PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network
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Learning data-driven discretizations for partial differential equations
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Lyapunov exponents of the Kuramoto–Sivashinsky PDE
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
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Learned discretizations for passive scalar advection in a 2-d turbulent flow
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Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics
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