セミナー・シンポジウム Seminars & Symposium

【5/20】AIMR Mini-workshop「材料科学分野のためのトポロジカルデータ解析」のご案内

AIMRミニワークショップ「材料科学分野のためのトポロジカルデータ解析」を企画しました。材料科学の問題にトポロジカルデータ解析を活用しておられる3名の講演者の少しずつ異なる切り口からのアプローチを知ることで、材料科学におけるトポロジカルデータ解析の姿を共有し、議論を深めたいと思います。皆様の積極的なご参加をお待ちしています。

日時

2026年5月20日（水）13:00～16:35

会場

AIMR本館 2階セミナールーム

言語

英語

プログラム

13:00～14:00	南谷 英美 教授（大阪大学）
14:00～14:20	Coffee Break
14:20～15:20	大林 一平 教授（岡山大学）
15:20～15:35	Coffee Break
15:35～16:35	赤木 和人 准教授（東北大学AIMR）

講演題目・要旨

南谷 英美 教授

Topological Descriptors for Inhomogeneous Systems via Persistent Homology

Understanding how structural inhomogeneity governs physical properties is an important challenge in materials science. In amorphous materials and glasses, structural motifs beyond the short-range atomic environment, often referred to as medium-range order, are known to play a crucial role. However, quantitatively characterizing such medium-range features and clarifying their connection to macroscopic properties remain nontrivial.
In this talk, I will discuss how persistent homology provides a useful framework for extracting multiscale topological information from atomistic configurations of amorphous and glassy materials. By combining persistence diagrams with statistical and machine-learning analyses, we can identify important structural motifs that are difficult to capture using conventional descriptors such as pair correlations or coordination statistics. I will present recent applications to covalent amorphous solids, where persistent-homology-based descriptors reveal how medium-range ring-like structures are linked to thermal and mechanical properties. These results suggest that persistent homology can serve not only as a predictive descriptor, but also as a physically interpretable tool for uncovering structure–property relationships in inhomogeneous materials.

大林 一平 教授

HomCloud: A Comprehensive Software Suite for Persistent Homology-Based Data Analysis

In this presentation, I will introduce persistent homology and HomCloud.
Persistent homology characterizes the shape of data using the mathematical idea of topology. Topological structures such as connected components, rings, and voids are used to summarize the shape of data quantitatively. Persistent homology is applied to various data from materials science, such as atomic configurations computed by molecular dynamics simulation and reverse Monte Carlo, and microscope images. Persistent homology is especially suitable for analyzing 3D structures and disordered structures.
HomCloud is the data analysis software based on persistent homology. HomCloud can analyze point cloud data, such as atomic configurations, and 2D or 3D binary or grayscale bitmaps, such as X-ray CT data, among other data types. HomCloud can compute persistence diagrams that summarize the shape information of the data, enabling further analysis of machine learning and inverse analysis.

赤木 和人 准教授

Topological Data Analysis of Microscopic Structures and Applications

Microscopic images captured via various techniques, such as Scanning Electron Microscopy (SEM), as well as large-scale and complex Molecular Dynamics (MD) simulation data, are thought to contain essential information that bridges the gap between microstructures and macroscopic properties in materials science. Persistent homology is a mathematical framework that describes the “birth” and “death” of “holes” within discrete datasets, including pixel images and atomic coordinates. Topological Data Analysis (TDA) leveraging this framework enables both the quantitative evaluation of “shapes” and a deeper understanding of the inherent order within a material's microstructure.
In this talk, I will provide a beginner-friendly introduction, using concrete examples, to how SEM images of metallic materials can be quantified through TDA and how these descriptors can be utilized as explanatory variables for mechanical properties. Furthermore, I will discuss methods for quantifying MD simulation data. I will also touch upon advanced efforts to extract “shapes” that align more closely with human intuition.

• [1] R. Muso et al., Persistent homology-based microstructural feature extraction and its correlation with mechanical properties in Mo-TiC alloys. Int. J. Refract. Met. Hard Mat. 138, 16 (2026).
• [2] X. C. Gao et al., Identification of microscopic structures in CFRP from X-ray CT based on topological data analysis. Sci. Technol. Adv. Mater.: Methods 5, 2572288 (2025).

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