Summary of Feature Mapping in Physics-informed Neural Networks (pinns), by Chengxi Zeng et al.
Feature Mapping in Physics-Informed Neural Networks (PINNs)
by Chengxi Zeng, Tilo Burghardt, Alberto M Gambaruto
First submitted to arxiv on: 10 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE)
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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 paper investigates the training dynamics of Physics-Informed Neural Networks (PINNs) with a feature mapping layer, exploring the convergence of PINNs in various scenarios. The study reveals that commonly used Fourier-based feature mapping is inadequate in certain physics contexts. To address this issue, the authors propose conditionally positive definite Radial Basis Function as an alternative. Empirical results demonstrate the efficacy of the method across diverse forward and inverse problem sets. The research highlights the importance of composing feature functions to balance expressivity and generalizability. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how Physics-Informed Neural Networks (PINNs) learn with a special kind of mapping called feature mapping. Researchers found that a popular way of doing this, based on fourier waves, doesn’t work well in some situations. To fix this, they suggest using a different type of map, called conditionally positive definite Radial Basis Function. They tested their idea and it worked well for many problems. This is an important discovery because it helps us make PINNs better at solving real-world problems. |
