Porosity and topological properties of triply periodic minimal surfaces

TL;DR

This paper explores the relationship between porosity, topological properties, and shape factors of triply periodic minimal surfaces (TPMS), proposing polynomial conjectures derived via machine learning, with implications for design and modeling.

Contribution

It introduces machine learning-based conjectures linking porosity and topology with shape factors in TPMS, advancing mathematical modeling techniques.

Findings

Proposes polynomial conjectures relating porosity and shape factors.

Integrates machine learning into pure mathematical research.

Provides models with potential applications in TPMS design.

Abstract

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.