Summary of Robust Identifiability For Symbolic Recovery Of Differential Equations, by Hillary Hauger et al.
Robust identifiability for symbolic recovery of differential equations
by Hillary Hauger, Philipp Scholl, Gitta Kutyniok
First submitted to arxiv on: 13 Oct 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 This paper explores the impact of noise on the discovery of physical laws governed by partial differential equations (PDEs). Machine learning has transformed this process, moving from manual derivation to data-driven methods that learn both structure and parameters. However, the non-uniqueness issue remains underexplored for algorithms that recover both simultaneously. The authors develop a comprehensive framework to analyze uniqueness in noisy scenarios and introduce new algorithms that account for noise. Numerical experiments demonstrate the effectiveness of these algorithms in detecting uniqueness despite noise. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Physical laws governed by partial differential equations (PDEs) can be discovered using machine learning. However, this process is affected by noise. Researchers have studied how noise affects parameter estimation but not when both structure and parameters are recovered simultaneously. This paper investigates how noise influences the discovery of PDEs. The authors develop a framework to analyze uniqueness in noisy scenarios and introduce new algorithms that account for noise. These algorithms can help scientists make reliable conclusions. |
Keywords
» Artificial intelligence » Machine learning
