mlsanityData to 14 Oct 2026

Physics and Data Driven Transformer-Mamba Framework for Flow Field

arXiv 2609.29087 ↗First posted 24 Sep 2026cs.LGcited by 0

On the map: State-space sequence models (S4, Mamba) → Time series forecasting with SSMs

Abstract (arXiv)

While deep learning accelerates expensive partial differential equation solving in computational fluid dynamics (CFD), existing methods like PINNs and FNOs often struggle with generalization, noise robustness, and physical consistency. We introduce the Transformer-Mamba for Flow Field (TM4FF) framework, a physics-constrained operator learning model with three key innovations: a Residual Wavelet Mamba (RWM) layer for feature denoising, a Transformer-based attention mechanism for enhanced feature fusion, and a physics-informed loss using Fourier derivatives to enforce the Navier-Stokes equations. Experiments on four CFD datasets show TM4FF achieves high accuracy and robust generalization across varying flow conditions.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba). Builds on 15 of its 26 references that are in the map. First posted on arXiv 24 Sep 2026.

Builds on

15 of 26 references.

References · 15

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2021TransUNet: Transformers Make Strong Encoders for Medical Image Segmentationcited by 1,558
  5. 2024Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Modelcited by 1,056
  6. 2024U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentationcited by 419
  7. 2024VM-UNet: Vision Mamba UNet for Medical Image Segmentationcited by 287
  8. 2023BiFormer: Vision Transformer with Bi-Level Routing Attentioncited by 151
  9. 2024Mamba-UNet: UNet-Like Pure Visual Mamba for Medical Image Segmentationcited by 133
  10. 2021Shunted Self-Attention via Multi-Scale Token Aggregationcited by 90
  11. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 38
  12. 2024Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networkscited by 21
3 more
  1. 2024Dual Cone Gradient Descent for Training Physics-Informed Neural Networkscited by 21
  2. 2023ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equationscited by 6
  3. 2023Learning from Integral Losses in Physics Informed Neural Networkscited by 4

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2024PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction
  2. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domains
  3. 2025FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model
  4. 2025GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations
  5. 2025Residual-augmented flow matching operators for probabilistic partial differential equations
  6. 2026Adaptive Mamba Neural Operators
  7. 2025FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fields
  8. 2024LE-PDE++: Mamba for accelerating PDEs Simulations