| Abstract: |
| In this talk, we present two hybrid methods for solving fluid dynamic equations, which combine neural network methods and traditional methods. The first is applying the asymptotic-preserving and positive-preserving techniques to physics-informed neural networks, which has advantages in high dimensionality and multiscale characteristics. The second is learning a class of new discretization schemes with neural networks, which has high accuracy in the smooth stencil and maintains essentially non-oscillation near the discontinuity. Numerical simulations are employed to validate our methods. |
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