# Physics and Data Driven Transformer-Mamba Framework for Flow Field > Source: > Published: 2026-09-25 04:00:00+00:00 # Physics and Data Driven Transformer-Mamba Framework for Flow Field By Zhuo Zhang, Shun Zou, Canqun Yang, Xi YangSource: [arXiv cs.LG](https://arxiv.org/list/cs.LG/recent) arXiv:2609.29087v1 Announce Type: new Abstract: While [deep learning](https://www.machinebrief.com/glossary/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](https://www.machinebrief.com/glossary/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](https://www.machinebrief.com/glossary/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. Get AI news in your inbox Daily digest of what matters in AI. ## Key Terms Explained Attention A mechanism that lets neural networks focus on the most relevant parts of their input when producing output. Attention Mechanism The attention mechanism is a technique that lets neural networks focus on the most relevant parts of their input when producing output. Deep Learning A subset of machine learning that uses neural networks with many layers (hence 'deep') to learn complex patterns from large amounts of data. Transformer The neural network architecture behind virtually all modern AI language models.