arXiv:2606. 24696v1 Announce Type: cross Abstract: Physics-informed surrogate models can accelerate computational fluid dynamics simulations.
By Somyajit Chakraborty, Ming Pan, Xizhong Chen
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
Field temporal prediction and source identification constitute canonical problems in dynamical systems. Conventional approaches to these problems depend on a thorough understanding of the governing pa...
arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.
By Till Muser, Alexandra Spitzer, Matti Lassas, Maarten V. de Hoop, Ivan Dokmani\'c
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
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.