Simulating physical systems using Partial Differential Equations (PDEs) has
become an indispensible part of modern industrial process optimization.
Traditionally, numerical solvers have been used to solve the associated PDEs,
however recently Transform-based Neural Operators such as the Fourier Neural
Operator and Wavelet Neural Operator have received a lot of attention for their
potential to provide fast solutions for systems of PDEs. In this work, we
investigate the importance of the transform layers to the reported success of
transform based neural operators. In particular, we record the cost in terms of
performance, if all the transform layers are replaced by learnable linear
layers. Surprisingly, we observe that linear layers suffice to provide
performance comparable to the best-known transform-based layers and seem to do
so with a compute time advantage as well. We believe that this observation can
have significant implications for future work on Neural Operators, and might
point to other sources of efficiencies for these architectures.

研究表明，使用可学习的线性层替代变换层可以在性能上与最佳的基于变换的层相媲美，并且在计算时间上具有优势，这对神经操作符的未来工作可能具有重要的影响，也可能指出这些架构的其他效率来源。