Efficient temporal prediction of compressible flows in irregular domains using Fourier neural operators

TL;DR

This paper presents a Fourier Neural Operator-based method combined with RNNs for efficient and accurate multi-step prediction of high-speed compressible flows in irregular domains, outperforming traditional numerical methods in speed and accuracy.

Contribution

The paper introduces a novel approach integrating Fourier Neural Operators with RNNs and a composite loss for multi-physical quantity prediction in irregular flow fields.

Findings

Achieves maximum relative $L_2$ errors of 0.78%, 0.57%, 0.35% for pressure, temperature, and velocity.

Significantly surpasses traditional numerical methods in computational efficiency.

Effectively models the temporal evolution of complex compressible flows in irregular geometries.

Abstract

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.