Viscous Regularization PINN Algorithm for Shallow Water Equations

doi:10.19596/j.cnki.1001-246x.8592

Abstract

Abstract:

Because of the shortcomings of classical PINN (Physical-informed Neural Networks) for discontinuous problems of shallow water equation, a regularized PINN algorithm based on viscous dissipative mechanism was proposed. In the network framework, the viscous regularized shallow water equation is used as the physical constraint and the penalty term in the loss function. Training network makes the smooth solution of the regularized equation approximate the discontinuous solution of the original equation. Finally, for one-dimensional and two-dimensional shallow water problems with different initial conditions, the numerical results show that the new algorithm has strong generalization ability, can predict the solution at any time, and has high resolution, without the phenomenon of spurious oscillation.

Key words: shallow water equation, PINN algorithm, viscous regularization, viscous vanishing solution

Supei ZHENG, Yunyun LIN, Jianhu FENG, Fang JIN. Viscous Regularization PINN Algorithm for Shallow Water Equations[J]. Chinese Journal of Computational Physics, 2023, 40(3): 314-324.

Figures/Tables 7

Fig.1 Diagrammatic sketch of PINN

Fig.2 Diagrammatic sketch of viscous regularization PINN

Fig.3 Results on Exp. 1 (a)results of the classical PINN algorithm; (b)results of the regularization PINN algorithm

Fig.4 Results on Exp. 2 (a)results of the classical PINN algorithm; (b)results of the regularization PINN algorithm

Fig.5 Results on Exp. 3(a)results of the classical PINN algorithm; (b)results of the regularization PINN algorithm

Fig.6 Results on Exp. 4(t=0.2) (a)results of the classical PINN algorithm; (b)results of the regularization PINN algorithm

Fig.7 Results on Exp. 5 (t=0.45) (a)results of the classical PINN algorithm; (b)results of the regularization PINN algorithm

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