Transport-generated signals uncover geometric features of evolving branched structures

Branched structures that evolve over time critically shape the function of diverse natural and engineered systems, from neuronal dendrites and vascular networks to pulmonary and root architectures. Inferring their hidden geometric properties and monitoring their morphological evolution remain major challenges, as direct imaging or tracer tracking is often infeasible, especially in living systems. Here, we introduce a general theoretical framework to recover the structural features of evolving branched geometries by analyzing the collective signals generated by tracer particles during transport. As tracers traverse the structure, they emit detectable pulses upon reaching an observation site. We show that the statistical properties of the resulting signal intensity, which reflects underlying first-passage dynamics, encode key morphological descriptors such as network extent, directional bias, and local trapping frequency. The strength of our approach lies in enabling quantitative inference of geometric parameters from time-series data recorded at a single observation site. This theoretical framework is designed to guide and motivate future experimental studies in systems where direct imaging is not feasible. Unlike conventional tracer-tracking methods, our approach enables noninvasive inference of hidden geometry solely from externally measurable signals, requiring no access to individual trajectories or internal measurements. This conceptual advance opens an avenue for transport-based structural inference and provides a scalable strategy for probing dynamic, complex architectures across biological, physical, and synthetic systems.