Learning Transient Convective Heat Transfer with Geometry Aware World Models

Abstract: Partial differential equation (PDE) simulations are fundamental to engineering and physics but are often computationally prohibitive for real-time applications. While generative AI offers a promising avenue for surrogate modeling, standard video generation architectures lack the specific control and data compatibility required for physical simulations. This paper introduces a geometry aware world model architecture, derived from a video generation architecture (LongVideoGAN), designed to learn transient physics. We introduce two key architecture elements: (1) a twofold conditioning mechanism incorporating global physical parameters and local geometric masks, and (2) an architectural adaptation to support arbitrary channel dimensions, moving beyond standard RGB constraints. We evaluate this approach on a 2D transient computational fluid dynamics (CFD) problem involving convective heat transfer from buoyancy-driven flow coupled to a heat flow in a solid structure. We demonstrate that the conditioned model successfully reproduces complex temporal dynamics and spatial correlations of the training data. Furthermore, we assess the model's generalization capabilities on unseen geometric configurations, highlighting both its potential for controlled simulation synthesis and current limitations in spatial precision for out-of-distribution samples.