Summary of Geometric Neural Operators (gnps) For Data-driven Deep Learning Of Non-euclidean Operators, by Blaine Quackenbush and Paul J. Atzberger
Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operators
by Blaine Quackenbush, Paul J. Atzberger
First submitted to arxiv on: 16 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Machine Learning (stat.ML)
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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 In this paper, researchers propose Geometric Neural Operators (GNPs) to account for geometric contributions in deep learning of operators. GNPs can be used to estimate geometric properties, approximate Partial Differential Equations on manifolds, learn solution maps for Laplace-Beltrami operators, and solve Bayesian inverse problems for identifying manifold shapes. The methods allow handling geometries of general shape including point-cloud representations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper introduces a new way to use geometry in deep learning. It shows how to use Geometric Neural Operators (GNPs) to do things like estimate geometric properties and solve equations on curves or surfaces. This can help us learn more about shapes and patterns in data. |
Keywords
» Artificial intelligence » Deep learning
