The talk focuses on data-driven analysis of the connection between the material structure and the systems' large-scale properties. The structure here may refer to the interactions (often formulated in terms of networks) forming spontaneously between granular particles, connectivity of the pores in porous media, or interactions between cells in tissue. The large-scale properties may focus on the rheology of flowing granular systems or suspensions, the material response of porous media to external forcing, or transport processes (such as fluid flow through porous matrix), among others. Independently of the context, the structure itself can be represented by established measures emerging from computational topology that allow for detailed but computationally efficient quantification. This approach allows for extracting precisely defined quantities that describe the structure and correlate it with the system's response. The example to be discussed involves interaction networks that spontaneously form in particulate-based systems. These networks, most commonly known as `force chains', are crucial for revealing the underlying causes of many physical phenomena involving material response, see [1-3] for examples of our recent works in this direction. The presentation will focus on applying topological data analysis (TDA), particularly persistent homology (PH). PH allows for a simplified representation of complex interaction fields in two and three dimensions (2D/3D) in terms of persistent diagrams that are essentially point clouds. These point clouds can be compared meaningfully, allowing for the data-driven analysis of the underlying systems' static and dynamic properties. The example to be considered involves experimental and simulation data related to an intruder moving in a stick-slip fashion through a 2D granular domain. We will focus, in particular, on exploring the predictability potential of the considered topological measures in the broader context of granular experiments and simulations.