Non-equispaced Fourier Neural Solvers for PDEs

ICLR 2023(2023)

引用 0|浏览20
暂无评分
摘要
Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is sometimes inevitably non-equispaced in real-world systems, limiting their applicability. In this paper, we propose a Non-equispaced Fourier PDE Solver (\textsc{NFS}) with adaptive interpolation on resampled equispaced points and a variant of Fourier Neural Operators as its components. Experimental results on complex PDEs demonstrate its advantages in accuracy and efficiency. Compared with the spatially-equispaced benchmark methods, it achieves superior performance with $42.85\%$ improvements on MAE, and is able to handle non-equispaced data with a tiny loss of accuracy. Besides, to our best knowledge, \textsc{NFS} is the first ML-based method with mesh invariant inference ability to successfully model turbulent flows in non-equispaced scenarios, with a minor deviation of the error on unseen spatial points.
更多
查看译文
关键词
Neural Operators,PDE Solvers
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络