用低维隐空间建模物理系统动态，揭示何时能准确预测未来状态。
When do World Models Successfully Learn Dynamical Systems?
- 将时间片段压缩为低维表示并拼接成历史序列，提升建模效率
- 在热方程、波动方程和卡门涡街等复杂流体场景中成功复现动态
- 从线性回归到生成对抗网络逐步验证方法有效性，适合物理模拟研究者
本文研究使用紧凑的隐空间表示与学习的时间动态（'World Models'）来模拟物理系统。基于控制理论思想，提出一个理论框架，解释为何将时间切片投影至低维空间并拼接形成历史序列（'Tokenization'）在学习物理数据集时如此有效，并刻画了在何种条件下，可由历史已知的编码帧重建下一时刻的状态。为验证上述观点，构建了一系列复杂度递增的模型：从最小二乘回归，到简单线性层、浅层对抗学习器，最终到全规模生成对抗网络（GAN）。在多种数据集上进行评估，包括改进的热方程、波动方程、二维柯尔莫哥洛夫-西瓦辛斯基混沌方程，以及一个具有挑战性的二维卡门涡街绕固定圆柱的计算流体动力学（CFD）数据集，结果显示模型能够成功重建流场演化。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。