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

2025-02-02

AI Summary

Convolutional autoencoders (CAEs) for image-sequence modeling often yield latent states that violate temporal continuity and deviate from true dynamical evolution. Method: We propose Continuity-Preserving Convolutional Autoencoders (CpAEs), which integrate a variational convolutional encoder, differential equation modeling in latent space, and explicit continuity regularization—specifically enforcing temporal smoothness of encoder convolutional kernels to ensure latent variables strictly obey continuous dynamical laws. Contribution/Results: Evaluated on diverse physical systems—including fluid dynamics, pendulum motion, and reaction–diffusion processes—CpAEs significantly improve temporal continuity and long-term prediction accuracy of latent trajectories. Average reconstruction error decreases by 37%, while generated trajectories exhibit enhanced physical interpretability and adherence to conservation laws. CpAEs thus establish a new paradigm for vision-based dynamical system modeling that balances theoretical rigor with practical efficacy.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Continuous Dynamical Systems
• Image Data
• Convolutional Autoencoders

Innovation

• Continuous Preservation
• Convolutional Autoencoders
• Dynamical Systems Learning