Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the loss function to enhance generalization performance. Since simulating dynamics controlled by partial differential equations (PDEs) can be computationally expensive, PINNs have gained popularity in learning parametric surrogates for fluid flow problems governed by Navier-Stokes equations. In this work, we introduce RANS-PINN, a modified PINN framework, to predict flow fields (i.e., velocity and pressure) in high Reynolds number turbulent flow regimes. To account for the additional complexity introduced by turbulence, RANS-PINN employs a 2-equation eddy viscosity model based on a Reynolds-averaged Navier-Stokes (RANS) formulation. Furthermore, we adopt a novel training approach that ensures effective initialization and balance among the various components of the loss function. The effectiveness of the RANS-PINN framework is then demonstrated using a parametric PINN.

翻译：物理信息神经网络（PINNs）提供了一种框架，用于构建受微分方程支配的动力系统的代理模型。在学习过程中，PINNs在损失函数中引入基于物理的正则化项，以增强泛化性能。由于模拟由偏微分方程（PDEs）控制的动力学问题可能在计算上十分昂贵，PINNs在学习受纳维-斯托克斯方程支配的流体流动问题的参数化代理模型方面已广受欢迎。在本工作中，我们引入了RANS-PINN——一种改进的PINN框架——用于预测高雷诺数湍流状态下的流场（即速度和压力）。为应对湍流引入的额外复杂性，RANS-PINN采用基于雷诺平均纳维-斯托克斯（RANS）公式的二方程涡黏性模型。此外，我们采用了一种新颖的训练方法，确保有效初始化并平衡损失函数各组成部分之间的权重。随后，通过一个参数化PINN示例展示了RANS-PINN框架的有效性。