Physics and Data Driven Transformer-Mamba Framework for Flow Field

2026-09-24

AI Summary

This study addresses the limited generalization, poor noise robustness, and insufficient physical consistency of deep learning in computational fluid dynamics (CFD) by proposing a physics-constrained operator learning framework that integrates Transformer and Mamba architectures. Methodologically, a residual wavelet Mamba layer is designed for feature denoising, while a Transformer module facilitates multi-scale feature fusion. Furthermore, a Fourier-based differential Navier-Stokes physical loss is incorporated to ensure solution consistency. Experimental results demonstrate that the proposed framework achieves high-accuracy flow field predictions across four CFD benchmark datasets and exhibits superior robust generalization capabilities under varying operating 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.

Problem

• Computational Fluid Dynamics
• Partial Differential Equations
• Generalization
• Noise Robustness
• Physical Consistency

Innovation

• Transformer-Mamba
• Residual Wavelet Mamba
• Physics-informed loss
• Operator learning
• Computational fluid dynamics