arXiv:2607.03198cs.LGmath-ph2026-07

世界模型的雏形早在几十年前就被物理系统实时控制领域实现并验证。

Reduced-Order Models: The Mother of World Models

  • 从降维建模中提取环境的低维隐状态,支持动作条件预测。
  • 通过解析误差界实现模型可信度验证,确保闭环控制安全。
  • 适合需要高可靠性、零容错的工业控制系统部署。

世界模型——一种支持动作条件预测与规划的环境压缩隐表示——通常被视为现代自监督学习的产物。本文指出,世界模型的功能结构早在几十年前就已在模型降维(MOR)与控制领域独立发展、应用并形式化分析,尽管名称不同、目标各异:服务于物理系统的实时运行。我们追溯三个领域的脉络:基于本征正交分解(POD)的湍流低维模型提供了从混沌环境数据中学习的隐动态;早期计算机视觉中的特征脸方法提供了编码-解码结构,包含原始的运行时有效性检验;基于测量的POD框架用于设施热控,则构建了完整闭环:POD系数作为隐状态,执行器设定值的参数依赖作为动作条件,模态重构作为解码,并关键地引入先验解析误差界作为验证层,确保模型在闭环中可信赖。随后分析各传统优势:MOR提供验证能力、物理根基和极高的数据效率;学习型世界模型则具备非线性表征、可迁移性和长程预测能力。我们主张,世界模型在不可容错系统(如电力、热控、过程控制)中部署的首要障碍并非预测精度,而是可验证性,并提出统一两大学派的物理基底、可验证世界模型研究议程。

原文摘要 · Abstract (English)

World models -- compressed latent representations of an environment that support action-conditioned prediction and planning -- are typically presented as a product of modern self-supervised learning. This paper argues that the functional anatomy of a world model was independently developed, deployed, and formally analyzed decades earlier in the model-order-reduction (MOR) and control literature, under different names and for a different purpose: the real-time operation of physical systems. We trace the anatomy across three communities. Low-dimensional models of turbulence built on proper orthogonal decomposition (POD) supplied latent dynamics learned from data of a chaotic environment; eigenface methods in early computer vision supplied the encoder-decoder half, including a primitive runtime validity check; and measurement-based POD frameworks for facility thermal control assembled the complete loop -- POD coefficients as latent state, parametric dependence on actuator setpoints as action conditioning, modal reconstruction as decoding, and, critically, a priori analytical error bounds as a verification layer that certified when the model's predictions could be trusted in closed loop. We then examine what each tradition possesses that the other lacks: MOR contributes verification, physical grounding, and extreme data efficiency; learned world models contribute nonlinear representation, transferability, and horizon. We argue that the outstanding obstacle to deploying world models in systems that cannot fail -- power, thermal, process control -- is not predictive fidelity but verifiability, and we outline a research agenda for physics-grounded, verifiable world models that unifies the two lineages.

世界模型降维建模控制理论可验证性

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