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Related Experiment Video

Updated: Jan 14, 2026

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Dimensionless learning based on information.

Yuan Yuan1, Adrián Lozano-Durán2,3

  • 1Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA. yuany999@mit.edu.

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|October 16, 2025
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Summary
This summary is machine-generated.

IT-π is a novel method for creating dimensionless variables using information theory. It identifies the most predictive variables, improving physical system understanding and model efficiency.

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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.