Challenges and Opportunities in Machine Learning for Geometry

Rafael Magdalena-Benedicto (), Sonia Pérez-Díaz and Adrià Costa-Roig
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Rafael Magdalena-Benedicto: Department of Electronic Engineering, University of Valencia, 46010 Valencia, Spain
Sonia Pérez-Díaz: University of Alcalá, Department of Physics and Mathematics, 28871 Alcalá de Henares, Spain
Adrià Costa-Roig: Department of Pediatric Surgery, La Fe University and Polytechnic Hospital, 46026 Valencia, Spain

Mathematics, 2023, vol. 11, issue 11, 1-24

Abstract: 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 generalized asymptotes.

Keywords: algebraic geometry; machine learning; generalized asymptotes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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