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Mutual-information-based dimensional learning: Objective algorithms for identification of relevant dimensionless quantities
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DOI：10.1016/j.cma.2025.117922.png)
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Abstract
En 中文
The classical dimensional analysis provides powerful insights into underlying physical mechanisms, but has limitations in determining the uniqueness and measuring the relative importance of dimensionless quantities. To address these limitations, we propose a data-driven approach, called mutual-information-based dimensional learning, to identify unique and relevant dimensionless quantities from available data. The proposed method employs a novel information- theoretic criterion to measure the relative importance of dimensionless quantities, whereas the existing methodologies rely on sensitivity/derivative-based measures. This entropy-based measure provides two significant advantages: (1) invariance (objectivity) with respect to reparametrizations of variables, and (2) robustness against outliers. Numerical results show that our method outperforms the current state-of-the-art method in these aspects, and enables identifying dominant dimensionless quantities. Examples include the study of the friction factor in benchmark pipe flows, the eddy viscosity coefficients in turbulent channel flows and the vapor depression dynamics in laser-metal interaction.
Keywords:
Data-driven dimensional analysis
Mutual information
Objectivity
Machine learning
Journal
IF:
7.3
Papers:
1.3W
Citations:
5.6W