Summary of Kolmogorov Arnold Informed Neural Network: a Physics-informed Deep Learning Framework For Solving Forward and Inverse Problems Based on Kolmogorov Arnold Networks, by Yizheng Wang et al.
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
by Yizheng Wang, Jia Sun, Jinshuai Bai, Cosmin Anitescu, Mohammad Sadegh Eshaghi, Xiaoying Zhuang, Timon Rabczuk, Yinghua Liu
First submitted to arxiv on: 16 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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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 A new neural network approach, called Kolmogorov-Arnold-Informed Neural Network (KINN), is proposed to solve partial differential equations (PDEs). This model builds upon the Physics-informed neural networks (PINNs) framework, but uses a different architecture, known as Kolmogorov-Arnold Networks (KAN), which offers interpretability and requires fewer parameters. The KINN approach is tested on various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Results show that KINN significantly outperforms the traditional MLP-based PINNs regarding accuracy and convergence speed for most PDEs in computational solid mechanics. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary AI helps solve partial differential equations (PDEs) better using a new type of neural network. This new approach, called Kolmogorov-Arnold-Informed Neural Network (KINN), is better than the old way because it’s more accurate and works faster. KINN uses a special kind of network that can be understood and doesn’t need as many parts. It tries to solve different types of PDE problems, like ones with lots of scales or complicated shapes. The results show that KINN does a great job solving most of these problems. |
Keywords
* Artificial intelligence * Neural network
