改进的物理融合神经网络在瑞利?泰勒不稳定性问题中的应用

基于相场法的物理融合神经网络PF-PINNs被成功用于两相流动的建模, 为两相流动的高精度直接数值模拟提供了全新的技术手段. 相场法作为一种新兴的界面捕捉方法, 其引入确保了界面的质量守恒, 显著提高了相界面的捕捉精度; 但是相场法中高阶导数的存在也降低了神经网络的训练速度. 为了提升计算训练过程的效率, 本文在PF-PINNS框架下, 参考深度混合残差方法MIM, 将化学能作为辅助变量以及神经网络的输出之一, 并修改了物理约束项的形式, 使辅助变量与相分数的关系式由硬约束转为了软约束. 上述两点改进显著降低了自动微分过程中计算图的规模, 节约了求导过程中的计算开销. 同时, 为了评估建立的PF-PINNS在雷诺数较高、计算量较大的场景中的建模能力, 本文将瑞利?泰勒RT不稳定性问题作为验证算例. 与高精度谱元法的定性与定量对比结果表明, 改进PF-PINNs有能力捕捉到两相界面的强非线性演化过程, 且计算精度接近传统算法, 计算结果符合物理规律. 改进前后的对比结果表明, 深度混合残差方法能够显著降低PF-PINNS的训练用时. 本文所述方法是进一步提升神经网络训练速度的重要参考资料, 并为探索高精度智能建模方法提供了全新的见解. 

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.