Similarity Learning with neural networks
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910643590791168 |
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| author | Sanfins, Gabriel Ramos, Fabio Naiff, Danilo |
| author_facet | Sanfins, Gabriel Ramos, Fabio Naiff, Danilo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Similarity Learning with neural networks Sanfins, Gabriel Ramos, Fabio Naiff, Danilo Machine Learning Data Analysis, Statistics and Probability Fluid Dynamics 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. |
| title | Similarity Learning with neural networks |
| topic | Machine Learning Data Analysis, Statistics and Probability Fluid Dynamics |
| url | https://arxiv.org/abs/2410.07214 |