用傅里叶神经算子高效预测不规则域中高速可压缩流体的演化。
Efficient temporal prediction of compressible flows in irregular domains using Fourier neural operators
- 将不规则流场点集转为序列输入，结合循环网络实现多步时序预测。
- 在三种不同网格配置下，压力、温度、速度相对误差最高仅0.78%、0.57%、0.35%。
- 适合需要快速高精度模拟复杂流场演化的工程与科研场景。
本文研究使用傅里叶神经算子（FNO）对不规则流动域中的高速可压缩流体进行时序演化建模。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）中引入时序打包技术实现多步预测。进一步设计复合损失函数以平衡不同物理量的误差。在三种不同类型的不规则流动域上开展实验，包括正交与非正交网格配置。通过物理分量损失曲线、流场可视化及物理剖面的综合分析，结果表明：该方法在计算效率上显著优于传统数值方法，同时保持高精度，对（压力、温度、速度）的最大相对$ L_2 $误差分别为（0.78, 0.57, 0.35）%。验证了该方法在不规则域中高效准确模拟高速可压缩流体时序演化的可行性。
原文摘要 · Abstract (English)
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.
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