THE APPLICATION OF MODIFIED PHYSICS-INFORMED NEURAL NETWORKS IN RAYLEIGH-TAYLOR INSTABILITY

Physics-informed neural networks for phase-field method (PF-PINNs) are successfully applied to the modeling of two-phase flow, and it provides a brand-new way for the high-accuracy direct numerical simulation of two-phase flow. As an emerging interface capturing method, the introduction of the phase-field method in two phase flow ensures mass conservation near the interface and significantly enhances the interface capturing accuracy. However, the high-order derivate introduced by the phase-field method decreases the efficiency of network training. To enhance the efficiency of the training process, this paper regards the chemical energy as an auxiliary parameter and one of the outputs of the proposed neural network and revises the loss functions of physics constrain in the PF-PINNs framework based on the deep mixed residual method (MIM), which transforms the relationship between the auxiliary parameter and the phase-field variable from hard constrain to soft constrain. The proposed improvements decrease the size of the computational graph generated in automatic differentiation significantly and the computational cost of calculating high-order derivates in automatic differentiation is reduced. Meanwhile, the Rayleigh-Taylor (RT) instability is tested to assess the modeling ability of the proposed PF-PINNs when the Reynolds number is high and an enormous amount of calculation is needed. Compared with the spectral element-based phase-field method qualitatively and quantitatively, modified PF-PINNs can capture the strong non-linear evolution process of the interface, and the accuracy of modified PF-PINNs reaches the accuracy of traditional numerical solver. The result of the proposed neural network fits the characteristic of RT instability well. Compared the modified PF-PINNs with the original PF-PINNs, the results indicate that the deep mixed residual method can reduce the training time of the original PF-PINNs notably. The proposed method in this paper is a valuable reference for improving the training speed of the neural network and gives a new insight into exploring the intelligent modeling method with high accuracy.