Dimensionless learning based on information
Creators
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1.
Massachusetts Institute of Technology
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2.
California Institute of Technology
Abstract
Dimensional analysis is one of the most fundamental tools for understanding physical systems. However, the construction of dimensionless variables, as guided by the Buckingham-π theorem, is not uniquely determined. Here, we introduce IT-π, a model-free method that combines dimensionless learning with the principles of information theory. Grounded in the irreducible error theorem, IT-π identifies dimensionless variables with the highest predictive power by measuring their shared information content. The approach is able to rank variables by predictability, identify distinct physical regimes, uncover self-similar variables, determine the characteristic scales of the problem, and extract its dimensionless parameters. IT-π also provides a bound of the minimum predictive error achievable across all possible models, from simple linear regression to advanced deep learning techniques, naturally enabling a definition of model efficiency. We benchmark IT-π across different cases and demonstrate that it offers superior performance and capabilities compared to existing tools. The method is also applied to conduct dimensionless learning for supersonic turbulence, aerodynamic drag on both smooth and irregular surfaces, magnetohydrodynamic power generation, and laser-metal interaction.
Copyright and License
© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Acknowledgement
A.L.-D. and Y.Y. acknowledge support from the National Science Foundation under grant No. 2140775 and grant No. 2317254, Early Career Faculty grant from NASA’s Space Technology Research Grants Program (grant No. 80NSSC23K1498) and MISTI Global Seed Funds.
Data Availability
The data generated in this study as well as the analysis code have been deposited in a Zenodo database61 under identifier https://doi.org/10.5281/zenodo.17080657.
Code Availability
The code for this work is available at https://github.com/ALD-Lab/IT_PI.
Supplemental Material
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s41467-025-64425-8.pdf
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Additional details
Identifiers
- PMID
- 41102193
- PMCID
- PMC12531322
Funding
- National Science Foundation
- CBET-2140775
- National Science Foundation
- CBET-2317254
- National Aeronautics and Space Administration
- 80NSSC23K1498
- Massachusetts Institute of Technology
- MISTI Global Seed Funds -
Dates
- Accepted
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2025-09-15