Machine learning, especially the use of neural netowrks, have shown great success in a broad range of applications. In recent years, we have also seen significant advancement in effective neural architectures for learning on more complex data, such as point sets (note that here, each input sample is a set of points) or graphs. Examples include DeepSet, Transformer and Sumformer. This facilitates the development of neural network based approaches to solve (potentially hard) geometric optimization problems, such as the minimum enclosing ball of an input set of points, in a data-driven manner. In this talk, I will describe some of our recent exploration in designing effective and efficient neural models for several geometric problems: (1) estimating the Wasserstein distance between two input point sets, and (2) a family of shape fitting problems (e.g, fitting minimal enclosing balls). Our goal is to have a neural network model of bounded size (independent to input size) that can approximately solve a target problem for input of arbitrary sizes. This talk is based on joint work with S. Chen, T. sidiropoulos and O. Ciolli.