研究人员提出EFNOs，解决了FNOs跨域迁移问题，在热方程和材料科学任务中表现优异。
欧几里得傅里叶神经算子(EFNOs)是一种与域无关的替代方案，解决了传统傅里叶神经算子(FNOs)在不同周期域间迁移的问题。EFNO通过将谱核参数化为物理波矢的连续函数，使算子能在不同形状和大小的周期域中一致作用。研究者在热方程和材料科学任务中评估了EFNO，展示了其在未见网格尺寸和域上的泛化能力。
Euclidean Fourier Neural Operators
Fourier neural operators (FNOs) provide an efficient framework for learning mappings between function spaces as they are, by construction, independent of the grid resolution at which they are trained and evaluated. However, FNOs are not independent of the periodic domain they are applied to: their discrete spectral weights are indexed by integer Fourier mode numbers, which correspond to physical wavevectors. When applied to a different domain, the same trained weights act at different wavevectors, and the FNO silently represents a different operator. This makes FNOs unsuitable for tasks where transfer across domains is crucial. We propose Euclidean Fourier neural operators~(EFNOs) as a domain-independent alternative to FNOs. By parameterizing the spectral kernel as a continuous function of the physical wavevector, the EFNO can learn operators that act consistently across periodic domains of varying shape and size. We evaluate the EFNO on a simple heat equation and on a practically relevant materials science task of learning exchange-correlation potentials across different crystal structures, and demonstrate that the EFNO is able to generalize to unseen grid sizes and domains.