This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and then embed temporal bundling technique within a recurrent neural network (RNN) for multi-step prediction. We further employ a composite loss function to balance errors across different physical quantities. Experiments are conducted on three different types of irregular flow fields, including orthogonal and non-orthogonal grid configurations. Then we comprehensively analyze the physical component loss curves, flow field visualizations, and physical profiles. Results demonstrate that our approach significantly surpasses traditional numerical methods in computational efficiency while achieving high accuracy, with maximum relative $L_2$ errors of (0.78, 0.57, 0.35)% for ($p$, $T$, $\mathbf{u}$) respectively. This verifies that the method can efficiently and accurately simulate the temporal evolution of high-speed compressible flows in irregular domains.

翻译：本文利用傅里叶神经算子（FNO）研究了高速可压缩流体在不规则流场中的时间演化。我们将不规则流场点集重构为符合FNO输入要求的序列格式，并在循环神经网络（RNN）中嵌入时间捆绑技术以实现多步预测。我们进一步采用复合损失函数来平衡不同物理量之间的误差。实验在三种不同类型的不规则流场上进行，包括正交与非正交网格配置。随后，我们全面分析了物理分量损失曲线、流场可视化结果以及物理剖面。结果表明，我们的方法在计算效率上显著超越传统数值方法，同时实现了高精度，对于（$p$, $T$, $\mathbf{u}$）的最大相对$L_2$误差分别为（0.78, 0.57, 0.35）%。这验证了该方法能够高效且准确地模拟高速可压缩流动在不规则域中的时间演化过程。