Summary of Adaptation Of Uncertainty-penalized Bayesian Information Criterion For Parametric Partial Differential Equation Discovery, by Pongpisit Thanasutives et al.
Adaptation of uncertainty-penalized Bayesian information criterion for parametric partial differential equation discovery
by Pongpisit Thanasutives, Ken-ichi Fukui
First submitted to arxiv on: 15 Aug 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 introduces an extension to the uncertainty-penalized Bayesian information criterion (UBIC) for efficient parametric partial differential equation (PDE) discovery in noisy situations. The extended UBIC uses quantified PDE uncertainty over different temporal or spatial points to prevent overfitting, unlike conventional information criteria that tend to select overly complex PDEs. The method computes the UBIC with data transformation based on power spectral densities to identify the governing parametric PDE and its varying coefficients (PDE coefficients). Numerical experiments demonstrate that the extended UBIC accurately identifies the true number of terms and their varying coefficients even in noisy situations. This approach has potential applications in various fields, including fluid dynamics, heat transfer, and population dynamics. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine trying to figure out a secret rule behind some data without knowing what it is. That’s kind of like what scientists do when they try to understand complex phenomena like weather or traffic patterns. In this paper, researchers created a new way to find the right equation that explains the data. They used something called “Bayesian information criterion” and made it better by adding more details about how uncertain the results are. This helps them avoid picking too complicated an equation. The new method worked well in simulations and could be useful for solving real-world problems like predicting weather or traffic patterns. |
Keywords
» Artificial intelligence » Overfitting
