This project explores the use of Topological Data Analysis (TDA), a rapidly growing field at the intersection of applied topology, computational geometry, and data science. The project aims to develop innovative mathematical and computational tools for monitoring, understanding, and predicting changes in complex systems through the analysis of spatial time-series data.
Topological Data Analysis (TDA) emerged around the beginning of the 21st century from developments in applied topology and computational geometry.
One of the major challenges in data analysis is determining the appropriate scale at which to study data. Traditional methods often rely on selecting a single scale or parameter, which can obscure important features.
TDA addresses this challenge through a multi-scale approach, treating scale as a parameter rather than a fixed constant. This allows data to be analyzed simultaneously across all scales, enabling researchers to make informed decisions about which structures and patterns are truly meaningful.
TDA provides powerful methods for:
The primary objective is to develop mathematical and computational tools based on TDA to monitor and evaluate spatial time-series data, identify the key factors driving change in complex systems, and construct future scenarios describing their evolution.
The research focuses on three major classes of data:
In these contexts, change may correspond to:
The project seeks to answer several fundamental questions:
A recent proof-of-concept study conducted with researchers from TWT Science & Innovation GmbH demonstrated the potential of these methods in predictive maintenance for aircraft engines.
The project is led by Florian Pausinger, member of CEMS.UL and professor in the Department of Mathematics at the Faculty of Sciences.
Professor Pausinger has been an active researcher in discrete and computational mathematics for more than fifteen years.
He obtained his PhD under the supervision of Herbert Edelsbrunner, one of the pioneers and founding figures of Topological Data Analysis.
```Our long-term vision is to establish CEMS.UL as the national competence center for Topological Data Analysis in Portugal.
We aim to create a forum where researchers from across Portugal can exchange ideas, collaborate on projects, and provide expertise to industry partners.
To achieve this vision, several initiatives are already underway:
To develop this initiative further, we seek support for:
These researchers will help explore the applicability of TDA across diverse domains and contribute to the development of innovative methodologies for understanding complex systems.
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