Mesh manipulation is central to Computational Fluid Dynamics (CFD). However, creating appropriate computational meshes often involves substantial manual intervention that has to be repeated each time the target shape changes. To address this problem, we propose an auto-decoder-based latent representation approach. Human prior knowledge is embedded into learned geometric patterns, which eliminates the need for further handcrafting. Furthermore, the resulting computational meshes are differentiable with respect to the model parameters, which makes it suitable for inclusion in end-to-end trainable pipelines. We apply the model on 2D airfoils to demonstrate its ability to handle various tasks.