Scientists and practitioners interested in TDA are often most familiar with Vietoris-Rips complexes built over point clouds, but many types of available data have a known domain, additional structure, or specific geometric hypotheses or outcomes. Filtrations that incorporate these properties can isolate topological signal from noise much more successfully, but it can be a challenge to balance simplicity and interpretability with descriptive power.

In this talk we will explore this tension with three discipline-specific applications: agent-based tumour-immune modeling, arctic melt-pond evolution, and anthropogenic feature detection in landscape data. For each, we craft filtrations tailored to the available information, assumptions, and hypotheses, and interpret the results. We highlight computational limits and scientific questions such as the interpretation of persistence diagrams, comparison with benchmark techniques, model fitting, and feature extraction.