LaM-SLidE: Latent Space Modeling of Spatial Dynamical Systems via Linked Entities

TL;DR

LaM-SLidE introduces a novel latent space modeling approach for spatial dynamical systems that maintains entity traceability while leveraging scalable generative techniques, improving efficiency and accuracy across domains.

Contribution

The paper presents LaM-SLidE, a method that combines entity traceability with scalable latent space generative modeling for complex dynamical systems.

Findings

Performs favorably in speed, accuracy, and generalizability

Maintains entity traceability in latent representations

Effective across multiple domains

Abstract

Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video generation, similar approaches are more difficult for most dynamical systems. Such systems -- from chemical molecule structures to collective human behavior -- are described by interactions of entities, making them inherently linked to connectivity patterns, entity conservation, and the traceability of entities over time. Our approach, LaM-SLidE (Latent Space Modeling of Spatial Dynamical Systems via Linked Entities), bridges the gap between: (1) keeping the traceability of individual entities in a latent system representation, and (2) leveraging the efficiency and scalability of recent advances in image and video generation, where pre-trained encoder and decoder enable generative modeling directly in latent space. The core idea of LaM-SLidE is the introduction of identifier representations (IDs) that enable the retrieval of entity properties and entity composition from latent system representations, thus fostering traceability. Experimentally, across different domains, we show that LaM-SLidE performs favorably in terms of speed, accuracy, and generalizability. Code is available at https://github.com/ml-jku/LaM-SLidE .