Dimensionless learning based on information

Area of Science:

• Physics
• Information Theory
• Dimensional Analysis

Background:

• Dimensional analysis is crucial for understanding physical systems.
• The Buckingham-π theorem guides dimensionless variable construction but lacks uniqueness.
• Existing methods may not fully exploit predictive power or identify distinct physical regimes.

Purpose of the Study:

• Introduce IT-π, a model-free method combining dimensionless learning and information theory.
• Identify dimensionless variables with the highest predictive power.
• Provide a framework for ranking variables, identifying regimes, and defining model efficiency.

Main Methods:

• IT-π leverages the irreducible error theorem and information theory principles.
• It measures shared information content to identify predictive dimensionless variables.
• The method ranks variables, detects physical regimes, and determines characteristic scales.

Main Results:

• IT-π successfully identifies and ranks dimensionless variables by predictability.
• The method uncovers self-similar variables and extracts key dimensionless parameters.
• It establishes a bound for minimum predictive error, enabling model efficiency assessment.

Conclusions:

• IT-π offers superior performance and capabilities compared to existing tools.
• The method is applicable to diverse physical systems, including supersonic turbulence and magnetohydrodynamics.
• IT-π enhances dimensionless learning and provides deeper insights into physical phenomena.