专用变换在神经算子中有多重要？
How important are specialized transforms in Neural Operators?
AI总结：
本文通过将基于变换的神经算子中的变换层替换为可学习线性层，发现线性层即可达到相当性能并具备计算时间优势，从而质疑专用变换层的关键作用。
摘要：
使用偏微分方程（PDEs）模拟物理系统，已成为现代工业过程优化中不可或缺的一部分。传统上，数值求解器一直被用于求解相关的PDEs；然而，近年来，基于变换的神经算子（例如Fourier Neural Operator和Wavelet Neural Operator）因其为PDEs系统提供快速解的潜力而受到广泛关注。在本研究中，我们考察了变换层对于基于变换的神经算子所报告成功的重要性。具体而言，我们记录了当所有变换层都被可学习线性层替换时，在性能方面所付出的代价。令人惊讶的是，我们观察到线性层足以提供与最知名的基于变换的层相当的性能，而且似乎还具有计算时间方面的优势。我们认为，这一观察结果可能对未来关于神经算子的研究产生重要影响，并可能指向这些架构的其他效率来源。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
