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

Yifan Nie, Qiaoxin Li

TL;DR

The paper tackles predicting the temporal evolution of high-speed compressible flows in irregular domains governed by the Euler equations. It introduces a Fourier Neural Operator–based surrogate that restructures irregular-grid data into sequential inputs and integrates temporal bundling within an RNN to enable multi-step forecasts, guided by a composite multi-physics loss. Key contributions include irregular-grid input restructuring for FNO, a joint FNO-RNN with time bundling (k=5), and a balanced loss that harmonizes pressure, temperature, and velocity predictions, achieving maximum relative $L_2$ errors of $$(0.78, 0.57, 0.35)\%$$ for $(p, T, \mathbf{u})$. Experiments on forward-step, cylinder, and airfoil geometries demonstrate substantial speedups over traditional solvers while maintaining high accuracy and generalization across non-orthogonal meshes, supporting rapid design evaluation for aerospace applications.

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.

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

TL;DR

The paper tackles predicting the temporal evolution of high-speed compressible flows in irregular domains governed by the Euler equations. It introduces a Fourier Neural Operator–based surrogate that restructures irregular-grid data into sequential inputs and integrates temporal bundling within an RNN to enable multi-step forecasts, guided by a composite multi-physics loss. Key contributions include irregular-grid input restructuring for FNO, a joint FNO-RNN with time bundling (k=5), and a balanced loss that harmonizes pressure, temperature, and velocity predictions, achieving maximum relative errors of for . Experiments on forward-step, cylinder, and airfoil geometries demonstrate substantial speedups over traditional solvers while maintaining high accuracy and generalization across non-orthogonal meshes, supporting rapid design evaluation for aerospace applications.

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 errors of (0.78, 0.57, 0.35)% for (, , ) respectively. This verifies that the method can efficiently and accurately simulate the temporal evolution of high-speed compressible flows in irregular domains.
Paper Structure (10 sections, 7 equations, 15 figures, 6 tables)

This paper contains 10 sections, 7 equations, 15 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. FNO
  4. Temporal Bundling
  5. Loss Function
  6. Numerical Experiments
  7. Forward Step
  8. Cylinder Flow
  9. Airfoil Flow
  10. Conclusion

Figures (15)

  • Figure 1: Computational grid and boundary labels of Forward step
  • Figure 2: Errors of Forward step
  • Figure 3: Physical field and absolute error of Forward step at $t = 1.8$ s
  • Figure 4: Multi-physics field predictions across $t=1.0-1.8$ s of Forward step
  • Figure 5: $T$ profiles of Forward step in $t=1.0-1.8$ s
  • ...and 10 more figures