{"ID":2897489,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04898","arxiv_id":"2507.04898","title":"When do World Models Successfully Learn Dynamical Systems?","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 so effective at learning physics datasets, and characterise when exactly the underlying dynamics admit a reconstruction mapping from the history of previous tokenized frames to the next. 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.","short_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...","url_abs":"https://arxiv.org/abs/2507.04898","url_pdf":"https://arxiv.org/pdf/2507.04898v2","authors":"[\"Edmund Ross\",\"Claudia Drygala\",\"Leonhard Schwarz\",\"Samir Kaiser\",\"Francesca di Mare\",\"Tobias Breiten\",\"Hanno Gottschalk\"]","published":"2025-07-07T11:29:18Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}