Abstract: Cosmological theories rely on understanding the three-dimensional structure of the Universe on large scale. Astrophysical observations of galaxy clusters are limited to measuring a two-dimensional position in the sky and a one-dimensional velocity along the line of sight, inherently losing part of the relevant information content. Commonly, the third spatial dimension is reconstructed by applying a deterministic scaling of the line-of-sight velocity that accounts for the expansion of the Universe (Hubble flow). However, due to gravitational effects, this transformation does not hold in the vicinity of massive structures, such as galaxy clusters. In this work, we propose an interpretable probabilistic model aiming to reconstruct the three-dimensional radial distance of an observed galaxy from its nearest galaxy cluster. Our model is completely transparent and it explicitly embeds astrophysical prior knowledge to account for the non- trivial dynamics that are superimposed on the Hubble flow. The three- dimensional radial distance is reconstructed in the form of a posterior distribution, conditioned on the positional and kinematical observations, which enables coherent quantification of the predicted uncertainties. We train our model on data from cosmological simulations, and we then use it to reconstruct the actual cluster neighbourhoods. We empirically show that our model is more accurate in recovering the radial profile of several simulated clusters, for which the ground truth is known, compared to the standard techniques. Crucially, our model-driven approach also uncovers features of simulated cosmological data that are not yet fully understood from a theoretical perspective, suggesting new directions of research. This tool is designed for use by astronomical observers, offering improvements over existing methods and opening up possibilities for further scientific discoveries.