# Similarity Learning with neural networks

arXiv: https://arxiv.org/abs/2410.07214 · HTML: https://mlsanity.com/paper/2410.07214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 28 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 3 of 3)

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Dimensionally Consistent Learning with Buckingham Pi](https://mlsanity.com/paper/2202.04643/) (2022)

## Abstract (arXiv)

In this work, we introduce a neural network algorithm designed to automatically identify similarity relations from data. By uncovering these similarity relations, our network approximates the underlying physical laws that relate dimensionless quantities to their dimensionless variables and coefficients. Additionally, we develop a linear algebra framework, accompanied by code, to derive the symmetry groups associated with these similarity relations. While our approach is general, we illustrate its application through examples in fluid mechanics, including laminar Newtonian and non-Newtonian flows in smooth pipes, as well as turbulent flows in both smooth and rough pipes. Such examples are chosen to highlight the framework's capability to handle both simple and intricate cases, and further validates its effectiveness in discovering underlying physical laws from data.