arXiv:2606. 24851v1 Announce Type: new Abstract: Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain.
By Jason Sulskis, Sathya Ravi
arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
By Alex Colagrande, Paul Caillon, Eva Feillet, Alexandre Allauzen
arXiv:2606. 27459v2 Announce Type: replace Abstract: We consider the cubic nonlinear Schr\"odinger (NLS) equation on two-dimensional flat tori with varying aspect ratios.
By Emmanuel E. Oguadimma, Victory C. Obieke, Xueying Yu
arXiv:2606. 27459v1 Announce Type: new Abstract: We consider the cubic nonlinear Schr\"odinger (NLS) equation on two-dimensional flat tori with varying aspect ratios.
By Emmanuel E. Oguadimma, Victory C. Obieke, Xueying Yu
Euclidean Fourier Neural Operators (EFNOs) extend Fourier neural operators by making the spectral kernel a continuous function of physical wavevectors, thereby removing dependence on specific periodic domain shapes and sizes. This domain‑independent formulation allows EFNOs to learn operators that generalize across different grid resolutions and domain geometries. Experiments on a heat equation and a materials‑science task demonstrate that EFNOs can successfully transfer learned mappings to unseen grid sizes and crystal structures.
By Nathanael Bosch, Niklas Frederik Schmitz, Michael F. Herbst
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
By Hang-Cheng Dong, Pengcheng Cheng