Categorization of incongruent TPMS by geometric features using manifold learning and clustering

Triply periodic minimal surface (TPMS) structures are architected porous materials derived from mathematically defined surfaces. These structures are of particular interest in many applications, mainly due to their high connectivity and smooth surfaces. In this study, 12 incongruent TPMS types (IWP, Lidinoid, OCTO, FRD, P+C(P), Split-P, G’, G’ 2 , D’, K, C(I 2 -Y**), and Slotted-P) are categorized based on their geometric features calculated over 9 porosities. A previously reported framework utilizing the uniform manifold approximation and projection (UMAP) algorithm for dimensionality reduction and the K-Means algorithm for clustering is modified to accommodate the asymmetric geometries of incongruent TPMS structures. The clustering analysis of 12 incongruent TPMS types yields four physically meaningful categories of incongruent TPMS structures. The modified framework further enables the comprehensive investigation of a combined dataset including both (i) congruent and (ii) incongruent TPMS types. The clustering analysis of this combined dataset yields similar distinct categorizations of congruent (previous work) and incongruent (this work) TPMS types, further demonstrating the promise of this framework for geometric design space exploration. No overlap of categories is found between congruent and incongruent TPMS types and, overall, congruent TPMS types are still recommended as the first choice for practical implementations due to the greater symmetry of their geometries.