Mesh-Free Convolution: Learned Spectral Attenuation and Transport
The research proposes Mesh-Free Convolutions (MFCs), continuous filters that learn scale-dependent smoothing and directional transport terms, unlike standard Fourier Neural Operators (FNOs) which use fixed spectral limits. MFCs enable stable long-horizon predictions in time-dependent PDEs like fluid dynamics by allowing learned filters to work across different resolutions and preserving fine spatial details.