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

arXiv 2601.01922 ↗First posted 5 Jan 2026physics.flu-dyn cs.LGcited by 0

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Abstract (arXiv)

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 L2 errors of (0.78, 0.57, 0.35)% for (p, T, 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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References · 17

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  6. 2022Message Passing Neural PDE Solverscited by 368
  7. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  8. 2017Recent Trends in Deep Learning Based Natural Language Processingcited by 262
  9. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 173
  10. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  11. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  12. 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
5 more
  1. 2019Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modelingcited by 40
  2. 2019DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy datacited by 38
  3. 2020Deep learning of free boundary and Stefan problemscited by 33
  4. 2020MeshingNet: A New Mesh Generation Method based on Deep Learningcited by 30
  5. 2023Physics-constrained robust learning of open-form partial differential equations from limited and noisy datacited by 8

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