MENO：内存高效的神经算子

中文摘要 AI 辅助

我们提出了内存高效的神经算子（MENO），这是一种基于流形函数编码器（MFE）的高性能偏微分方程神经求解器。MENO具有三个主要优势：（1）与其他流行架构相比，MENO的内存占用显著更小，训练速度更快，且内存占用与数据分辨率无关，因此有望扩展到大规模模型。（2）MENO可以接受任意形式的偏微分方程输入，包括任意几何域和任意离散化。特别地，它能够处理跨几何场景，即输入函数和输出解定义在不同流形上的情况。（3）MENO展现出强大的泛化能力，在我们测试的大多数基准上，与文献中报告的结果相比，取得了最佳精度。代码可在GitHub上获取，网址为https://github.com/jpzxshi/MENO，本文中的所有数值示例均可通过单条命令运行以复现报告的结果。

英文摘要

We propose the Memory-Efficient Neural Operator (MENO) as a high-performance PDE neural solver based on the Manifold Function Encoder (MFE). MENO features three primary advantages: (1) MENO has a significantly smaller memory footprint and much faster training speed than other popular architectures, with the memory footprint being independent of the data resolution, and therefore holds the potential for scaling up to large-scale models. (2) MENO can accept PDE inputs of arbitrary form, including arbitrary geometric domains and arbitrary discretizations. In particular, it is capable of handling cross-geometry scenarios, i.e., where the input functions and the output solutions are defined on different manifolds. (3) MENO exhibits strong generalization capability, and achieves the best accuracy on most of the benchmarks we tested, compared with the results reported in the literature. The code is available on GitHub at https://github.com/jpzxshi/MENO, and all numerical examples in this paper can be run with a single command to reproduce the reported results.

发表机构

• Peking University（北京大学）
• National Engineering Laboratory for Big Data Analysis and Applications, Peking University（北京大学大数据分析与应用技术国家工程实验室）
• Chongqing Research Institute of Big Data, Peking University（北京大学重庆大数据研究院）

机构由 AI 辅助整理，请以论文原文为准。