arXiv Machine Learning By Zhuo Zhang, Shun Zou, Canqun Yang, Xi Yang

Physics and Data Driven Transformer-Mamba Framework for Flow Field

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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.

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arXiv Machine Learning
Sep 10

Local gradient neural operator

The paper introduces the Local Gradient Neural Operator (LGNO), a lightweight and interpretable neural operator designed for field temporal evolution prediction and source identification in mechanical problems. LGNO leverages nonlinear gradient discretization priors and multilayer perceptron convolutional layers to learn translation‑invariant local kernels resembling discrete stencils, with a zero‑consistent stencil factorization that separates coefficient learning from field reconstruction. Experiments on a range of PDE benchmarks—including linear, nonlinear, static, dynamic, low‑ and high‑dimensional cases—demonstrate that LGNO achieves comparable accuracy to global neural operators while using fewer parameters and maintaining rollout stability across diffusion, flow, and quantum phenomena.

By Baiming Zhang, Jinsong Tang, Ying Xu, Lihua Chen, Shiying Xiong
arXiv Machine Learning
Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.

By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
Hugging Face Trending Papers
Jun 4

On the training of physics-informed neural operators for solving parametric partial differential equations

Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.