论文标题
Navier-Stokes方程的螺旋保守物理知识的神经网络模型
Helicity-conservative Physics-informed Neural Network Model for Navier-Stokes Equations
论文作者
论文摘要
在理想情况下，我们为Navier-Stokes方程设计了螺旋能保守的物理信息神经网络模型。关键是提供适当的PDE模型作为损耗函数，以便其神经网络解决方案产生螺旋性保护。物理信息神经网络模型基于PDE的强大形式。我们比较了提出的物理知识的神经网络模型和相关的螺旋性保守有限元方法。我们得出的结论是，强大的PDE形式更适合保护问题。我们还提供了有关螺旋性保护的理论理由以及支持数值计算。
We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce helicity conservation. Physics-informed neural network model is based on the strong form of PDE. We compare the proposed Physics-informed neural network model and a relevant helicity-conservative finite element method. We arrive at the conclusion that the strong form PDE is better suited for conservation issues. We also present theoretical justifications for helicity conservation as well as supporting numerical calculations.
