Speaker
Description
Metamaterials are artificial and architected materials, offering various possible designs for achieving peculiar mechanical properties thanks to their structural arrangement. Although promising, with potentially broad applications in, e.g., medicine [1] or mobility [2], apprehending their geometry is challenging due to their complex and often disordered configuration. In this regard, applied topology and its tools, such as persistent homology [3], emerged as a great mathematical method to grasp their geometrical organization and to use it in the design and inverse design of metamaterials. Indeed, persistent homology allows the local geometry of the structure to be captured and converted into point clouds representing the structural features. In other words, the geometrical problem is translated into a data analysis problem, suitable for statistical methods, for example via machine learning models [4]. We discuss the application of persistent homology to point patterns [5] and we show that the resulting data, although obtained from local geometrical features, can capture with great accuracy global properties only appearing on large scales, for instance, the hyperuniformity of the arrangement [6]. We illustrate how the persistent homology delivers an exploitable description of the geometry, and we expose different data analysis methods that can be applied, ranging from machine learning to minimization processes including the Wasserstein distance. Finally, we discuss the highly promising extensions offered by these results to the case of hyperuniform fields, with a large range of applications to the mechanical engineering of metamaterials.
[1] Masoud Shirzad, Ali Zolfagharian, Mahdi Bodaghi, Seung Yun Nam, Enhanced manu-facturing possibilities using multi-materials in laser metal deposition, European Journalof Mechanics - A/Solids, volume 98, (2023)
[2] Anastasiia Krushynska, Metamaterials in flexible wings, Society of Acoustics (2024)
[3] Gunnar Carlsson, Topology and data, Bull. Amer. Math. Soc. 46, 255-308 (2009)
[4] Pun, Chi Seng and Lee, Si Xian and Xia, Kelin, Persistent-homology-based machinelearning: a survey and a comparative study, Artif. Intell. Rev. 55, 5169-5213 (2022)
[5] Abel H. G. Milor, Marco Salvalaglio, Inferring hyperuniformity from local structuresvia persistent homology arXiv preprint (arXiv:2409.08899) (2024)
[6] Salvatore Torquato, Hyperuniform states of matter, Physics Reports volume 745, 1-95(2018)
