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.

翻译：偏微分方程（PDE）模拟是工程学和物理学的基础，但其计算成本往往过高，难以满足实时应用需求。尽管生成式人工智能为代理建模提供了有前景的途径，但标准的视频生成架构缺乏物理模拟所需的特定控制和数据兼容性。本文提出一种源自视频生成架构（LongVideoGAN）的几何感知世界模型架构，专门用于学习瞬态物理过程。我们引入了两个关键架构要素：（1）包含全局物理参数和局部几何掩码的双重条件调节机制；（2）支持任意通道维度的架构适配，突破了标准RGB约束的限制。我们在一个涉及浮力驱动流与固体结构热流耦合的二维瞬态计算流体动力学（CFD）对流换热问题上评估了该方法。实验表明，该条件调节模型成功复现了训练数据中复杂的时空动力学特征与空间相关性。此外，我们评估了模型在未见几何构型上的泛化能力，既揭示了其在可控模拟合成方面的潜力，也指出了当前对于分布外样本在空间精度上的局限性。