Summary of Structure-preserving Physics-informed Neural Networks with Energy or Lyapunov Structure, by Haoyu Chu et al.
Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure
by Haoyu Chu, Yuto Miyatake, Wenjun Cui, Shikui Wei, Daisuke Furihata
First submitted to arxiv on: 10 Jan 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 Recently, physics-informed neural networks (PINNs) have gained attention as a promising approach to solving differential equations. However, the preservation of underlying structure, such as energy and stability, has yet to be systematically addressed. This limitation may hinder efficient learning processes and result in nonphysical behavior. To address these issues, we propose structure-preserving PINNs that leverage prior knowledge about physical systems to design a structure-preserving loss function. This framework also utilizes PINNs for robust image recognition by preserving the Lyapunov structure of the underlying system. Experimental results demonstrate improved numerical accuracy for partial differential equations and enhanced robustness against adversarial perturbations in image data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Scientists are trying to use a new type of artificial intelligence called physics-informed neural networks (PINNs) to solve complex math problems. The problem is that these models don’t always behave like the real-world systems they’re trying to describe. To fix this, researchers propose a new approach that helps PINNs learn more accurately and apply to different areas like image recognition. By using prior knowledge about how real-world systems work, they can design a loss function that makes sure the model stays true to those underlying rules. This leads to better results in math problems and also makes the model more resistant to fake data. |
Keywords
* Artificial intelligence * Attention * Loss function
