Summary of Rbf-pinn: Non-fourier Positional Embedding in Physics-informed Neural Networks, by Chengxi Zeng et al.
RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks
by Chengxi Zeng, Tilo Burghardt, Alberto M Gambaruto
First submitted to arxiv on: 13 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 This paper explores the limitations of Fourier-based feature mapping in Physics-Informed Neural Networks (PINNs) and proposes an alternative approach using conditionally positive definite Radial Basis Functions. By highlighting the benefits of this new method, researchers can improve their PINN models’ performance across various forward and inverse problem scenarios. The study’s findings demonstrate the effectiveness of this approach in enhancing the empirical benefits of feature mapping, which is essential for advancing the field of PINNs. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A team of researchers has looked at how to make Neural Networks better at solving math problems. They found that a common way of doing this called Fourier-based feature mapping isn’t always the best. Instead, they suggest using something called Radial Basis Functions. This new method works well for many kinds of problems and can be used with other techniques to make PINNs (Physics-Informed Neural Networks) even better. |
