Problem
Research questions and friction points this paper is trying to address.
Memory-Efficiency
Neural Operator
PDE Solver
MENO: Memory-Efficient Neural Operator
🤖 AI Summary
提出MENO作为高效PDE神经求解器，通过Manifold Function Encoder实现低内存占用、快速训练及处理任意几何域和离散化问题的能力。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Memory-Efficient
Neural Operator
Arbitrary Geometries
Cross-Geometry Scenarios
Strong Generalization
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