When do World Models Successfully Learn Dynamical Systems?

Edmund Ross, Claudia Drygala, Leonhard Schwarz, Samir Mani Kaiser, Francesca di Mare, Tobias Breiten, Hanno Gottschalk

Keywords: world models, turbulence, GANs, observability, time dynamics, control theory, cfd

Abstract: In this work, we explore the use of compact latent representations with learned time dynamics ('World Models') to simulate physical systems. Drawing on concepts from control theory, we propose a theoretical framework that explains why projecting time slices into a low-dimensional space and then concatenating to form a history ('Tokenization') is effective at learning dynamical systems, and characterise when the underlying dynamics admit a reconstruction mapping from the history of previous tokenized frames to the next, with the key novel insight being observability. To validate these claims, we develop a sequence of models with increasing complexity, starting with least-squares regression and progressing through simple linear layers, shallow adversarial learners, and ultimately full-scale generative adversarial networks (GANs). We evaluate these models on a variety of datasets, including modified forms of the heat and wave equations, the chaotic regime 2D Kuramoto-Sivashinsky equation, and a challenging computational fluid dynamics (CFD) dataset of a 2D Kármán vortex street around a fixed cylinder, where our model is successfully able to recreate the flow. Comparisons to FNO and DeepONet show comparable short- and improved long-term accuracy.

Primary Area: learning theory

Submission Number: 12926