Summary of A Comprehensive and Fair Comparison Between Mlp and Kan Representations For Differential Equations and Operator Networks, by Khemraj Shukla et al.
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
by Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang, Zongren Zou, George Em Karniadakis
First submitted to arxiv on: 5 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Physics (physics.comp-ph)
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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 Kolmogorov-Arnold Networks (KANs) are an alternative representation model to Multilayer Perceptron (MLP). The paper proposes using KANs to create physics-informed machine learning models and deep operator models for solving differential equations. This includes comparing KAN-based models, such as PIKANs and DeepOKANs, with physics-informed neural networks (PINNs) and deep operator networks (DeepONets), which are based on standard MLP representation. The results show that modified KAN versions have comparable performance to PINNs and DeepONet, but lack robustness due to potential divergence for different random seeds or higher-order orthogonal polynomials. The paper also visualizes loss landscapes and analyzes learning dynamics using information bottleneck theory. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Kolmogorov-Arnold Networks (KANs) are a new way of representing data. In this study, scientists used KANs to create special kinds of models that can solve math problems involving changes over time or space. They compared these models with other types of models that do the same thing, like physics-informed neural networks and deep operator networks. The results show that some versions of KAN-based models work just as well as the others, but they might not be reliable in all situations. This study also looked at how the models learn and what happens when they encounter different kinds of math problems. |
Keywords
» Artificial intelligence » Machine learning
