mlsanityData to 7 Oct 2026

A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling

arXiv 2606.24696 ↗First posted 23 Jun 2026physics.flu-dyn cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of 2.70 × 10-4, compared with 4.02 × 10-4 for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 32 of its 49 references that are in the map. First posted on arXiv 23 Jun 2026.

Builds on

32 of 49 references.

References · 32

  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. 2021Choose a Transformer: Fourier or Galerkincited by 333
  4. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  5. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  6. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  7. 2021BERT: A Review of Applications in Natural Language Processing and Understandingcited by 109
  8. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  9. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  10. 2023Residual-based attention in physics-informed neural networkscited by 72
  11. 2023Diffusion-Based Adversarial Sample Generation for Improved Stealthiness and Controllabilitycited by 66
  12. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
20 more
  1. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 54
  2. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  3. 2023CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamicscited by 40
  4. 2024Continuum Attention for Neural Operatorscited by 39
  5. 2020Hierarchical Deep Learning of Multiscale Differential Equation Time-Stepperscited by 37
  6. 2024Wavelet Diffusion Neural Operatorcited by 28
  7. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  8. 2024Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspectivecited by 24
  9. 2023Physics Informed Token Transformer for Solving Partial Differential Equationscited by 21
  10. 2024Physics-Informed Geometry-Aware Neural Operatorcited by 18
  11. 2023Multi-scale Time-stepping of Partial Differential Equations with Transformerscited by 14
  12. 2026RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Datacited by 13
  13. 2024Masked Autoencoders are PDE Learnerscited by 11
  14. 2025Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Studycited by 11
  15. 2024Physics-Informed Neural Networks and Extensionscited by 8
  16. 2025MeshMask: Physics-Based Simulations with Masked Graph Neural Networkscited by 8
  17. 2025FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modelingcited by 8
  18. 2024On the Effectiveness of Neural Operators at Zero-Shot Weather Downscalingcited by 4
  19. 2025Transforming physics-informed machine learning to convex optimizationcited by 2
  20. 2024Physics-embedded Fourier Neural Network for Partial Differential Equationscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Modular Deep Learning Mechanisms for Auditable Next-Day Wildfire Spread Predictioncited by 0
  2. 2026Do Better Scores Mean Better Physics? Physics-Grounded Explanations for Sim2Real Neural Operatorscited by 0