GAMM2025

Session

MS03: Topological Data Analysis

MS03

10 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

MS03: Topological Data Analysis: MS03.01

• Bartosz Naskręcki
• Paweł Dłotko

MS03: Topological Data Analysis: MS03.02

• Bartosz Naskręcki
• Paweł Dłotko

710. Improving descriptors and understandings in Material Sciences using TDA

Jan F. Senge

10/04/2025, 08:30

Topological Data Analysis (TDA) introduces innovative approaches for interpreting high-dimensional data by leveraging underlying structures and relationships. TDA uncovers qualitative similarities and differences, offering a unique perspective in various applications. In particular, the concept of persistence diagram vectorization enhances Machine Learning (ML) algorithms by providing an...

708. Topological Analysis of Dynamical Systems

Marta Marszewska

10/04/2025, 08:50

Dynamical systems analysis plays a crucial role in understanding the behavior of complex phenomena across various fields, including engineering, physics, and biology. However, the inherent complexity of these systems often presents significant challenges in their analysis, such as non-linearity and high-dimensionality. Topological methods have emerged as a powerful toolkit for addressing these...

706. Quantifying time-series similarity using topological conjugacy and related concepts

Justyna Signerska-Rynkowska

10/04/2025, 09:30

A key concept in comparison and classification of dynamical systems is the notion of topological conjugacy. In the talk we will consider a problem of testing topological (semi-)conjugacy of two trajectories coming from unknown dynamical systems when only finite samples of those trajectories are given. A number of tests and various numerical examples indicating their scalability and robustness...

711. Bifiltrations of Dowker complexes and their applications

Jan Spaliński

10/04/2025, 09:50

The Dowker complex of a relation was introduced by C.H. Dowker in 1952. Given a relation R on X times Y, the Dowker complex D(X, Y, R) is a simplical complex with vertex set X, and a subset sigma of X forms a simplex, if there is a y in Y with which every element of sigma is in relation. The number of such elements y is called the `weight' of the simplex. Although the construction has...

707. Classifying and predicting behaviours of porous structures using Topological Data Analysis

Michał Bogdan

10/04/2025, 14:00

Metallic porous materials are used in wide-ranging practical applications, from lightweight metal structures to medical implants. However, their use in a given application depends on obtaining the desired mechanical properties, such as Young’s modulus and yield stress. Advances in 3D printing enable the creating a wider choice of prescribed structures than ever before. However, to take...

709. Prediction of elastic modulus for metallic porous materials using 3D convolution neural networks

Rafał Topolnicki

10/04/2025, 14:20

The talk will present results on predicting the elastic properties of metallic 3D porous materials using convolutional networks and additional structural descriptors. Even for relatively small datasets, the developed machine learning models achieve a prediction accuracy of Young’s modulus at R² ≥ 0.95 across a wide range of porous structures. The reference Young’s modulus values were obtained...

712. Reeb graphs and the shape of space

Łukasz Michalak

10/04/2025, 14:40

A Reeb graph is a discrete invariant of a function on a space that provides information about the evolution of topology of the level sets. It is formed as the quotient of the space by contracting connected components of level sets of the function. Under sufficiently nice assumptions, e.g. for smooth functions on closed manifolds with finitely many critical values, it actually has the structure...

713. From Mathematical Theory to Machine Learning: Detecting Symmetry Groups in Crystallographic Tilings

Bartosz Naskręcki

10/04/2025, 15:00

This project explores the intersection of mathematics, crystallography, and machine learning by developing a method to detect symmetry groups of tilings (crystals). The approach originates from a mathematical technique I introduced in [1], which can be effectively modeled using classical machine learning methods. The work aligns with the principles of explainable AI, as preliminary results...