Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images
This addresses a specific issue in modeling continuous dynamical systems from image data for scientific and engineering applications, but it is incremental as it builds on existing convolutional autoencoder methods.
The paper tackled the problem of learning continuous latent dynamical models from discrete image frames, where naive convolutional autoencoders produce discontinuous latent states, and proposed continuity-preserving convolutional autoencoders (CpAEs) to resolve this, resulting in more accurate models as demonstrated in experiments.
Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as images, resulting in pixel-level observations that are discrete in nature. Consequently, a naive application of a convolutional autoencoder can result in latent coordinates that are discontinuous in time. To resolve this, we propose continuity-preserving convolutional autoencoders (CpAEs) to learn continuous latent states and their corresponding continuous latent dynamical models from discrete image frames. We present a mathematical formulation for learning dynamics from image frames, which illustrates issues with previous approaches and motivates our methodology based on promoting the continuity of convolution filters, thereby preserving the continuity of the latent states. This approach enables CpAEs to produce latent states that evolve continuously with the underlying dynamics, leading to more accurate latent dynamical models. Extensive experiments across various scenarios demonstrate the effectiveness of CpAEs.