Neural solver uses less memory and works on any shape
MENO: Memory-Efficient Neural Operator
Machine Learning
Summary
Solving partial differential equations (PDEs) is important in many fields like engineering and physics, but often requires lots of computer memory and limited data formats. The authors introduce MENO, a neural network method that uses much less memory and runs faster than previous methods. It can handle PDE problems on any kind of shape or grid, even when inputs and outputs differ in shape. MENO also performs very accurately across many test problems compared to other methods.
What this means in practice
- •For computational engineers: Use MENO to solve complex PDE problems on irregular or varying geometries with reduced memory and faster training times.
- •For simulation software developers: Integrate MENO as a scalable and accurate PDE solver component that handles high-resolution data without increasing memory usage.
Authors
Shengyang Xu, Weijun Zhang, Jun Hu, Pengzhan Jin
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.