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 regime. 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 RANS-PINN framework is then demonstrated using a parametric PINN.

翻译：物理信息神经网络（PINNs）为构建受微分方程控制的动力系统代理模型提供了框架。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。由于模拟偏微分方程（PDEs）控制的动力学过程计算成本高昂，PINNs在纳维-斯托克斯方程控制的流体问题参数化代理模型学习中受到广泛关注。本研究提出改进的PINN框架RANS-PINN，用于预测高雷诺数湍流工况下的流场（即速度与压力）。为应对湍流引入的额外复杂度，RANS-PINN采用基于雷诺平均纳维-斯托克斯（RANS）公式的两方程涡粘模型。此外，我们提出一种新型训练方法，确保有效初始化并平衡损失函数各组成部分。最后通过参数化PINN验证了RANS-PINN框架的有效性。