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This research advances operator learning in computational fluid dynamics by hybridizing Transformer attention with Mamba state-space mechanisms to enforce physical consistency via Navier-Stokes constraints. The framework demonstrates improved generalization and noise robustness over existing PINN and FNO methods, addressing key limitations in accelerating partial differential equation solving.
Physics and Data Driven Transformer-Mamba Framework for Flow Field
arXiv:2609.29087v1 Announce Type: new Abstract: 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.
Abstract: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.
Corrected version of our ICASSP'26 paper: Corrected seven Dam/MISSFormer metrics in Table 1 that were mistakenly estimated using the MSE(u) ratio. The conclusions remain unchanged
Machine Learning (cs.LG)
arXiv:2609.29087 [cs.LG]
(or arXiv:2609.29087v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.29087 arXiv-issued DOI via DataCite (pending registration)
https://doi.org/10.1109/ICASSP55912.2026.11460626 DOI(s) linking to related resources
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