Summary of Enhancing Symbolic Regression and Universal Physics-informed Neural Networks with Dimensional Analysis, by Lena Podina et al.
Enhancing Symbolic Regression and Universal Physics-Informed Neural Networks with Dimensional Analysis
by Lena Podina, Diba Darooneh, Joshveer Grewal, Mohammad Kohandel
First submitted to arxiv on: 24 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 new method presented combines Ipsen’s and Buckingham pi methods to enhance symbolic regression for differential equations. The goal is to reduce the number of input variables, simplify the search space, and ensure derived equations are physically meaningful. This is achieved by integrating dimensional analysis with Universal Physics-Informed Neural Networks (UPINNs) and AI Feynman symbolic regression algorithm. The results show that dimensionless data reduces computation time and improves accuracy. Buckingham pi theorem also helps in reducing complexity for algebraic equations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Symbolic regression often struggles with high computational costs and overfitting. To solve this, researchers used dimensional analysis to reduce the number of input variables and simplify the search space. They combined Ipsen’s method with Universal Physics-Informed Neural Networks (UPINNs) to identify hidden terms more effectively. The results show that using dimensionless data makes it easier to find accurate equations, even when there is limited data. |
Keywords
» Artificial intelligence » Overfitting » Regression
