Non-equispaced Fourier Neural Solvers for PDEs

Understand

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.