Challenges and Opportunities in Machine Learning for Geometry
Over the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/11/2576 |
| _version_ | 1797597069113819136 |
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| author | Rafael Magdalena-Benedicto Sonia Pérez-Díaz Adrià Costa-Roig |
| author_facet | Rafael Magdalena-Benedicto Sonia Pérez-Díaz Adrià Costa-Roig |
| author_sort | Rafael Magdalena-Benedicto |
| collection | DOAJ |
| description | Over the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector machines, and principal component analysis. Therefore, we consider as disruptive the use of machine learning algorithms to study mathematical structures, enabling the formulation of conjectures via numerical algorithms. In this paper, we review the latest applications of machine learning in the field of geometry. Artificial intelligence can help in mathematical problem solving, and we predict a blossoming of machine learning applications during the next years in the field of geometry. As a contribution, we propose a new method for extracting geometric information from the point cloud and reconstruct a 2D or a 3D model, based on the novel concept of <i>generalized asymptotes.</i> |
| first_indexed | 2024-03-11T03:01:34Z |
| format | Article |
| id | doaj.art-596c1dc1a98a42d29260359bb5a35e6f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:01:34Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-596c1dc1a98a42d29260359bb5a35e6f2023-11-18T08:13:55ZengMDPI AGMathematics2227-73902023-06-011111257610.3390/math11112576Challenges and Opportunities in Machine Learning for GeometryRafael Magdalena-Benedicto0Sonia Pérez-Díaz1Adrià Costa-Roig2Department of Electronic Engineering, University of Valencia, 46010 Valencia, SpainUniversity of Alcalá, Department of Physics and Mathematics, 28871 Alcalá de Henares, SpainDepartment of Pediatric Surgery, La Fe University and Polytechnic Hospital, 46026 Valencia, SpainOver the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector machines, and principal component analysis. Therefore, we consider as disruptive the use of machine learning algorithms to study mathematical structures, enabling the formulation of conjectures via numerical algorithms. In this paper, we review the latest applications of machine learning in the field of geometry. Artificial intelligence can help in mathematical problem solving, and we predict a blossoming of machine learning applications during the next years in the field of geometry. As a contribution, we propose a new method for extracting geometric information from the point cloud and reconstruct a 2D or a 3D model, based on the novel concept of <i>generalized asymptotes.</i>https://www.mdpi.com/2227-7390/11/11/2576algebraic geometrymachine learninggeneralized asymptotes |
| spellingShingle | Rafael Magdalena-Benedicto Sonia Pérez-Díaz Adrià Costa-Roig Challenges and Opportunities in Machine Learning for Geometry Mathematics algebraic geometry machine learning generalized asymptotes |
| title | Challenges and Opportunities in Machine Learning for Geometry |
| title_full | Challenges and Opportunities in Machine Learning for Geometry |
| title_fullStr | Challenges and Opportunities in Machine Learning for Geometry |
| title_full_unstemmed | Challenges and Opportunities in Machine Learning for Geometry |
| title_short | Challenges and Opportunities in Machine Learning for Geometry |
| title_sort | challenges and opportunities in machine learning for geometry |
| topic | algebraic geometry machine learning generalized asymptotes |
| url | https://www.mdpi.com/2227-7390/11/11/2576 |
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