Harnessing Topology and Causal Discovery for Dynamic Analysis and Particulate Gel Control

Particulate gels, characterized by multi-scale structures and dynamic behaviors, present significant challenges for quantitative analysis and control due to their evolving complexity under external stimuli. In this work, we integrate topological data analysis (TDA) and causal discovery methodologies to analyze particulate gels subjected to cyclic shear deformation. Utilizing persistence homology, we extract meaningful topological features across various scales, capturing critical structural transitions. These features are further processed through the Automatic Topologically-Oriented Learning (ATOL) algorithm, enabling their representation in a low-dimensional vector space suitable for causal analysis. Employing a VARLiNGAM causal discovery framework, we uncover multi-scale causal relationships, illustrating both top-down and bottom-up flows of structural information within the gel network. Our approach offers insights into the hierarchical organization and dynamic evolution of particulate gels, paving the way for enhanced predictive modeling and control strategies applicable to advanced soft material systems.