Regensburg 2025 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter

DY 27.11: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

Detection and Analysis of Topological Defgnetic Systems via Enhanced Topological Data Analysisects in Ma — •Kyra Klos¹, Karin Everschor-Sitte², and Friederike Schmid¹ — ¹Insitute of Physics, Johannes Gutenberg-University Mainz, Mainz, Germany — ²Faculty of Physics & Center for Nanointegration Duisburg-Essen, University of Duisburg-Essen, Duisburg, Germany

Complex data structures, marked by multi-dimensional correlations and noise, pose significant challenges in various fields like genetics and complex dynamical quantum systems. Topological Data Analysis (TDA) [1], rooted in Persistent Homology can address this, e.g. by effective characterizing phase transitions in dynamical systems [2], enhancing large genome data analysis [3] and preprocessing data for machine learning [1]. By introducing series of graph structures into data point clouds intrinsic topological information can be extracted. Focusing on magnetic systems with topological defects, localized perturbations in the ordering field, we propose using TDA to enhance their detection and analysis. By combing conventional persistence diagram analysis with geometrical, topological, and graph-based measures applied directly to the representative clustering, our approach can provide an additional insight into the topological landscape and multi-scale nature of topological defects in magnetic systems.

[1] F. Hensel et al., Frontiers in AI, vol. 4 (2021)

[2] E. Cheng et al., IOP, vol.57 [30] (2024)

[3] S. Yara et al, Journal of Biomedical Informatics, vol. 130 (2022)

Keywords: Topological Defects; Vortices; Topological Data Analysis; Graph Representation