The paper introduces the Transformer-Mamba for Flow Field (TM4FF), a physics-constrained operator learning model designed to improve partial differential equation solving in computational fluid dynamics. TM4FF incorporates a Residual Wavelet Mamba layer for feature denoising, a Transformer-based attention mechanism for enhanced feature fusion, and a physics-informed loss that enforces the Navier-Stokes equations using Fourier derivatives. Experiments on four CFD datasets demonstrate that TM4FF achieves high accuracy and robust generalization across varying flow conditions.
By Zhuo Zhang, Shun Zou, Canqun Yang, Xi Yang
arXiv:2605. 08832v3 Announce Type: replace Abstract: Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields.
By Jonas Weidner, Yeray Martin-Ruisanchez, Daniel Rueckert, Benedikt Wiestler, Julian Suk
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
arXiv:2607. 02715v1 Announce Type: new Abstract: Recently, neural operators have shown promising outcomes for learning solution operators of differential equations directly from data.
By Himanshu Pandey, Subham Patel, Ratikanta Behera
arXiv:2510.01365v2 Announce Type: replace
Abstract: The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted...
By Maedeh Saberi, Amir Barati Farimani, Safa Jamali
arXiv:2607. 22280v2 Announce Type: replace-cross Abstract: Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics.
By Harish Ramachandran, Bj\"orn Kimpel, Thomas Paula, Josef Winter, Steffen Schmidt, Nikolaus Adams
arXiv:2606. 16765v1 Announce Type: new Abstract: Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks.
By Lukas Schr\"oder, Shubham Kavane, Harald K\"ostler
arXiv:2512. 07847v2 Announce Type: replace Abstract: Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols.
By Mohamed Elrefaie, Dule Shu, Matt Klenk, Faez Ahmed
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
By Gabriel F. Barros, R\^omulo M. Silva, Alvaro L. G. A. Coutinho
arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.
By Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
By Ofek Aloni, Barak Fishbain
arXiv:2608.27883v1 Announce Type: new
Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...
By Rajat Sarkar, Venkataramana Runkana, Souvik Chakraborty