Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Understand

Partial differential equations (PDEs) are central to describing complex physical system simulations.

• Their expensive solution techniques have led to an increased interest in deep neural network based surrogates.
• However, the practical utility of training such surrogates is contingent on their ability to model complex multi-scale spatio-temporal phenomena.
• Various neural network architectures have been proposed to target such phenomena, most notably Fourier Neural Operators (FNOs), which give a natural handle over local & global spatial information via parameterization of different Fourier modes, and U-Nets which treat local and global information via downsampling and upsampling paths.