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

TL;DR

This paper introduces continuity-preserving convolutional autoencoders (CpAEs) that learn continuous latent dynamical models directly from image data, addressing the discontinuity issues of traditional autoencoders and improving modeling accuracy.

Contribution

The paper proposes a novel CpAE framework that promotes filter continuity to ensure smooth latent state evolution from image sequences, advancing the modeling of continuous dynamical systems.

Findings

CpAEs produce continuous latent states aligning with underlying dynamics.

The approach outperforms previous methods in modeling accuracy.

Extensive experiments validate the effectiveness of CpAEs.

Abstract

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.