Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images

Main contributation ▶ We propose a mathematical formulation for learning continuous dynamics from image data to describe the continuity of latent states. ▶ We demonstrate that the latent states will evolve continuously with the underlying dynamics if the filters are Lipschitz continuous. ▶ We introduce a regularizer to promote the continuity of filters and, consequently, preserve the continuity of the latent states. ▶ We perform several experiments across various scenarios to verify the effectiveness of the proposed method.