Topological Data Analysis for Complex Systems: Applications in Chemical Engineering

Datasets can be abstracted as mathematical objects (e.g., point clouds, matrices, graphs, images, manifolds) that have shape. This shape often represents intrinsic characteristics of the data and provides powerful insight into structure-function relationships within physical systems. In this talk, we explore the application of topological data analysis (TDA) to reveal hidden structures in complex systems across diverse fields in chemical engineering.

We focus on three key areas: molecular dynamics (MD) simulations, soft gel characterization, and industrial textile process monitoring. MD simulations produce highly intricate datasets that capture molecular interactions in 3D space. We show that the Euler characteristic, a topological descriptor, serves as an effective tool for reducing and analyzing this data, enabling better prediction of phenomena such as hydrophobicity and reactivity in chemical systems.

TDA is also employed to study the multi-scale structure of soft gels, materials known for their flexibility and resilience. We present a framework that combines TDA with dimensionality reduction techniques to quantify the local and global organization of gels, aiding in the understanding of their mechanical behavior under stress. Finally, we extend this analysis to industrial textiles, using TDA to detect defects in manufacturing processes. These examples highlight the versatility of TDA in simplifying complex data, providing new insights into system behavior and enhancing process understanding.