Summary of Leray-schauder Mappings For Operator Learning, by Emanuele Zappala
Leray-Schauder Mappings for Operator Learning
by Emanuele Zappala
First submitted to arxiv on: 2 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This research proposes an algorithm for learning operators between Banach spaces, utilizing Leray-Schauder mappings to approximate compact subspaces. The method is shown to be a universal approximator of possibly nonlinear operators, achieving comparable results to state-of-the-art models on two benchmark datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper develops an algorithm to learn operators between Banach spaces. It uses Leray-Schauder mappings to approximate compact subspaces and shows the resulting method can universally approximate operators, linear or non-linear. The approach is tested on two benchmark datasets and performs similarly to top models in the field. |
