MENO：内存占用与分辨率无关的 PDE 神经求解器
MENO: Memory-Efficient Neural Operator
一个开源的 PDE 神经求解器 MENO，显存不随分辨率涨，还能跨几何求解，跑论文实验只需一行命令。
论文提出基于 Manifold Function Encoder 的神经算子 MENO，用于求解 PDE。其内存占用不随数据分辨率增长，训练速度和显存开销低于 FNO、DeepONet 等主流架构。MENO 支持任意几何域和离散化输入，可处理输入函数与输出解定义在不同流形上的跨几何场景。作者在多个公开基准上取得优于文献已报告结果的精度，代码在 GitHub 开源且可一键复现。
MENO: Memory-Efficient Neural Operator
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.
