Data-rich 3D CAD models are essential during different life-cycle stages of engineering projects. Due to the recent popularization of Build Information Modeling methodology and the use of Digital Twins for intelligent manufacturing, the amount of detail, size, and complexity of these models have significantly increased. Although these models are composed of several repeated geometries, plant-design software usually does not provide any instancing information. Previous works have shown that removing redundancy in the representation of 3D CAD models significantly reduces their storage and memory requirements, whilst facilitating rendering optimizations. This work proposes a deep-learning-based shape-matching framework that minimizes a 3D CAD model s redundant information in this regard. We rely on recent advances in the deep processing of point clouds, overcoming drawbacks from previous work, such as heavy dependency on vertex ordering and topology of triangle meshes. The developed framework uses uniformly sampled point clouds to identify similarities among meshes in 3D CAD models and computes an optimal affine transformation matrix to instantiate them. Results on actual 3D CAD models demonstrate the value of the proposed framework. The developed point-cloud-registration procedure achieves a lower surface error while also performing faster than previous approaches. The developed supervised-classification approach achieves equivalent results compared to earlier, limited methods and significantly outperformed them in a vertex shuffling scenario. We also propose a selfsupervised approach that clusters similar meshes and overcomes the need for explicitly labeling geometries in the 3D CAD model. This self-supervised method obtains competitive results when compared to previous approaches, even outperforming them in certain scenarios.