The project will investigate the usage of Partial Differential Equations (PDEs) in neural networks. Specifically, we are interested in using PDEs to describe the latent traversal paths of the latent space of a given generative model. The key idea is to model the path using PDEs such that only one variation factor of the reconstruction is changing (e.g., the mouth of a face).This will benefit existing pre-trained generative models with more fine-grained and precise user control on the image attributes. Moreover, the project would also investigate training neural networks with PDE priors on the hidden units. Such a constrained prior could endow the neural network with better equivariance property, which will facilitate the real-world deployment and application of deep learning models.