We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth distances for the similarity assessment of scalar and vectorial data, produced from transport and motion-based simulations. Utilizing two data acquisition methods derived from this model, we create collections of fields from numerical PDE solvers and existing simulation data repositories. Furthermore, a multiscale CNN architecture that computes a volumetric similarity metric (VolSiM) is proposed and its robustness is evaluated on a large range of test data. To the best of our knowledge this is the first learning method inherently designed to address the similarity assessment of high-dimensional simulation data.