(645c) Topology-Driven Discovery of Multi-Scale Dynamics in Particulate Gels

Particulate gels are networked soft materials that exhibit complex dynamics and hierarchical structure across spatial and temporal scales [1]. These systems, composed of colloidal particles that self-assemble into connected networks, respond to deformation through a coupled evolution of microstructural and mesoscale features. Capturing and modeling this behavior remains a major challenge due to the system’s nonlinear, high-dimensional nature [2,3]. In this work, we develop a data-driven causal modeling framework that uncovers directional interactions between structural features across scales and time in particulate gels subjected to cyclic shear deformation.

Using molecular dynamics simulations, we track the evolution of gel structure as the system is driven through the nonlinear deformation regime [4]. Structural information is extracted using persistent homology, a tool from topological data analysis (TDA) that quantifies features such as loops and voids. These features are mapped to low-dimensional vectors using the Automatic Topologically-Oriented Learning (ATOL) algorithm, which enables analysis of structural changes over time [5,6].

We apply the Vector Auto-Regressive LiNGAM (VARLiNGAM) algorithm to the resulting time series to infer causal relationships between topological features [7,8]. The model identifies both time-lagged and instantaneous interactions, revealing a bidirectional flow of structural influence: large-scale voids drive local bond rearrangements, while microscale structural changes feed back into larger-scale organization. This hierarchical structure-dynamics relationship provides a mechanism-level understanding of how deformation propagates through soft material networks.

The causal model developed in this work captures dynamic, interpretable relationships between physically meaningful structural features. It provides a compact, structured description of system dynamics that can be integrated into control frameworks such as model predictive control (MPC) or reinforcement learning (RL) [9,10]. In doing so, it enables improved monitoring and regulation of soft materials in dynamic process environments.

In summary, we present a scalable, interpretable framework for constructing causal models of multi-scale dynamics in soft particulate systems. The approach links simulation data with dynamic systems modeling and opens new pathways for the control and optimization of structurally complex soft materials.

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[10] M. Sader, Y. Wang, D. Huang, C. Shang, and B. Huang, “Causality-informed data-driven predictive control,” IEEE Trans. Control Syst. Technol., 2025.