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

Generative models are spearheading recent progress in deep learning, showing strong promise for trajectory sampling in dynamical systems as well. However, while 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 and the traceability of entities over time. Our approach, LaM-SLidE (Latent Space Modeling of Spatial Dynamical Systems via Linked Entities), combines the advantages of graph neural networks, i.e., the traceability of entities across time-steps, with the efficiency and scalability of recent advances in image and video generation, where pre-trained encoder and decoder are frozen to enable generative modeling in the latent space. The core idea of LaM-SLidE is to introduce identifier representations (IDs) to allow for retrieval of entity properties, e.g., entity coordinates, from latent system representations and thus enables 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)