2024/06/23 by Sergei Ermolenko, Ermolenko, Sergei, Pavel Snopov +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #K-Theory and Homology (math.KT) #Machine Learning (stat.ML) #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2406.16215
openalex publication_date 2024/06/23 · openalex created_date 2024/06/27 · openalex updated_date 2026/07/28
Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships between porosity and persistence entropy with the shape factor of TPMS. We propose conjectures suggesting that these relationships are polynomial in nature, derived through the application of machine learning techniques. This study exemplifies the integration of machine learning methodologies in pure mathematical research. Besides the conjectures, we provide the mathematical models that might have the potential implications for the design and modeling of TPMS structures in various practical applications.