Summary of Learning Solution Operators Of Pdes Defined on Varying Domains Via Mionet, by Shanshan Xiao et al.
Learning solution operators of PDEs defined on varying domains via MIONet
by Shanshan Xiao, Pengzhan Jin, Yifa Tang
First submitted to arxiv on: 23 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed method learns solution operators of partial differential equations (PDEs) defined on varying domains using MIONet, with theoretical justification. By extending MIONet’s approximation theory to metric spaces, the method can approximate mappings with multiple inputs in various spaces. A set of regions is constructed and a metric is provided, satisfying MIONet’s approximation condition. This foundation allows learning the solution mapping of PDEs with varying parameters, including differential operator, right-hand side term, boundary condition, and domain. Experiments are performed on 2D Poisson equations with varying domains and right-hand side terms, providing insights into performance across different scenarios. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us solve special math problems called partial differential equations (PDEs). They’re used to model many things in science and engineering, like heat flow or water movement. The problem is that PDEs often have moving parts that make them hard to solve. This paper introduces a new way to learn how to solve these PDEs using something called MIONet. It’s flexible and can be used for different types of problems. The researchers tested it on some simple examples and showed that it works well. |
