  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.
