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降阶模型:世界模型之母

Reduced-Order Models: The Mother of World Models

Rajat Ghosh

arXiv 2607.03198首次发表:更新:

发表机构

Independent Researcher(独立研究员)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

探讨世界模型的功能结构早于现代自监督学习,在模型降阶和控制文献中就已独立发展。追溯其在三个领域的发展,对比传统降阶模型与学习型世界模型的优缺点,指出在关键系统中部署世界模型的障碍及统一两者的研究议程。

AI 中文摘要

世界模型是支持动作条件预测和规划的环境压缩潜在表示,通常被视为现代自监督学习的产物。本文认为其功能结构早在几十年前就在模型降阶和控制文献中以不同名称、出于不同目的(物理系统实时运行)独立开发、部署和正式分析。我们追溯了三个社区的结构,对比了传统降阶模型和学习型世界模型的优缺点,并提出了统一两者的研究议程。

英文摘要

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.

论文原文

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