Purpose

Physics-informed neural networks (PINNs) have become a new tendency in flow simulation, because of their self-advantage of integrating both physical and monitored information of fields in solving the Navier–Stokes equation and its variants. In view of the strengths of PINN, this study aims to investigate the impact of spatially embedded data distribution on the flow field results around the train in the crosswind environment reconstructed by PINN.

Design/methodology/approach

PINN can integrate data residuals with physical residuals into the loss function to train its parameters, allowing it to approximate the solution of the governing equations. In addition, with the aid of labelled training data, PINN can also incorporate the real site information of the flow field in model training. In light of this, the PINN model is adopted to reconstruct a two-dimensional time-averaged flow field around a train under crosswinds in the spatial domain with the aid of sparse flow field data, and the prediction results are compared with the reference results obtained from numerical modelling.

Findings

The prediction results from PINN results demonstrated a low discrepancy with those obtained from numerical simulations. The results of this study indicate that a threshold of the spatial embedded data density exists, in both the near wall and far wall areas on the train’s leeward side, as well as the near train surface area. In other words, a negative effect on the PINN reconstruction accuracy will emerge if the spatial embedded data density exceeds or slips below the threshold. Also, the optimum arrangement of the spatial embedded data in reconstructing the flow field of the train in crosswinds is obtained in this work.

Originality/value

In this work, a strategy of reconstructing the time-averaged flow field of the train under crosswind conditions is proposed based on the physics-informed data-driven method, which enhances the scope of neural network applications. In addition, for the flow field reconstruction, the effect of spatial embedded data arrangement in PINN is compared to improve its accuracy.

中文翻译：

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基于物理信息神经网络研究嵌入式数据分布策略对侧风影响列车周围流场重建精度的影响

 目的

物理信息神经网络（PINN）因其在求解纳维-斯托克斯方程及其变体时集成场的物理信息和监测信息的自身优势而成为流动模拟的新趋势。鉴于PINN的优势，本研究旨在研究空间嵌入数据分布对PINN重建的侧风环境下列车周围流场结果的影响。

设计/方法论/途径

PINN可以将数据残差和物理残差整合到损失函数中来训练其参数，使其能够逼近控制方程的解。此外，借助标记的训练数据，PINN还可以在模型训练中融入流场的真实场地信息。鉴于此，采用PINN模型，借助稀疏流场数据，在空间域上重建侧风作用下列车周围的二维时均流场，并将预测结果与参考结果进行比较来自数值模型。

 发现

PINN 结果的预测结果与数值模拟获得的结果差异较小。本研究的结果表明，在列车背风侧的近壁和远壁区域以及近列车表面区域都存在空间嵌入数据密度的阈值。换句话说，如果空间嵌入数据密度超过或低于阈值，就会对 PINN 重建精度产生负面影响。此外，本文还获得了重建侧风下列车流场时空间嵌入数据的最佳排列。

 原创性/价值

在这项工作中，提出了一种基于物理信息数据驱动方法重建侧风条件下列车时间平均流场的策略，扩大了神经网络的应用范围。另外，对于流场重建，比较了PINN中空间嵌入数据排列的效果，以提高其精度。