Triangular surface meshes are a widespread representation in 3D shape applications and a variety of neural network (NN) architectures have been developed in the recent years to handle them directly. However, with the advent of additive manufacturing, shapes with internal structures gain ever more significance, motivating the need for NN architectures capable of processing representations that admit disconnected boundaries. For analysis tasks, a potential solution is to extend existing NN architectures to handle tetrahedral volumetric meshes. On the other hand, generative tasks pose a greater challenge with both surface and volumetric meshes being restricted to a fixed topology. NNs representing implicit level-set functions offer greater topological flexibility but can also produce unwanted disconnected components. This talk will explore early-stage ideas on NN architectures for handling tetrahedral volumetric meshes, imposing shape connectivity on NNs representing implicit level-set functions and, finally, interoperability of NNs and PDE solvers for shape and topology optimization as a particular generative task.