The physics-informed neural network (PINN) method is extended to learn and predict compressible steady-state aerodynamic flows with a high Reynolds number. To better learn the thin boundary layer, the sampling distance function and hard boundary condition are explicitly introduced into the input and output layers of the deep neural network, respectively. A gradient weight factor is considered in the loss function to implement the PINN methods based on the Reynolds averaged Navier–Stokes (RANS) and Euler equations, respectively, denoted as PINN–RANS and PINN–Euler. Taking a transonic flow around a cylinder as an example, these PINN methods are first verified for the ability to learn complex flows and then are applied to predict the global flow based on a part of physical data. When predicting the global flow based on velocity data in local key regions, the PINN–RANS method can always accurately predict the global flow field including the boundary layer and wake, while the PINN–Euler method can accurately predict the inviscid region. When predicting the subsonic and transonic flows under different freestream Mach numbers (Ma∞= 0.3–0.7), the flow fields predicted by both methods avoid the inconsistency with the real physical phenomena of the pure data-driven method. The PINN–RANS method is insufficient in shock identification capabilities. Since the PINN–Euler method does not need the second derivative, the training time of PINN–Euler is only 1/3 times that of PINN–RANS at the same sampling point and deep neural network.

中文翻译：

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用于高雷诺数圆柱体周围跨音速流动的物理信息神经网络

物理信息神经网络（PINN）方法被扩展用于学习和预测具有高雷诺数的可压缩稳态空气动力流。为了更好地学习薄边界层，采样距离函数和硬边界条件分别显式地引入深度神经网络的输入层和输出层。在损失函数中考虑梯度权重因子，以实现基于雷诺平均纳维-斯托克斯（RANS）和欧拉方程的PINN方法，分别表示为PINN-RANS和PINN-Euler。以围绕圆柱体的跨音速流为例，这些 PINN 方法首先验证了学习复杂流的能力，然后应用于基于部分物理数据的全局流预测。在根据局部关键区域的速度数据预测全局流时，PINN-RANS方法总能准确预测包括边界层和尾流在内的全局流场，而PINN-Euler方法可以准确预测无粘区域。在预测不同自由流马赫数（Ma∞=0.3~0.7）下的亚音速和跨音速流动时，两种方法预测的流场都避免了纯数据驱动方法与真实物理现象的不一致。 PINN-RANS方法的冲击识别能力不足。由于PINN-Euler方法不需要二阶导数，因此在相同采样点和深度神经网络下，PINN-Euler的训练时间仅为PINN-RANS的1/3倍。