🤖 AI Summary
This work addresses the lack of verifiability in learned world models when deployed in high-assurance systems by proposing a novel framework that integrates classical model order reduction (MOR) with modern world modeling. The approach combines proper orthogonal decomposition (POD) with an encoder–decoder architecture, incorporates physics-informed error bounds derived from physical priors, and employs measurement-driven action-conditioned modeling to ensure verifiable closed-loop predictions, exceptional data efficiency, and physical consistency. By systematically unifying MOR theory with contemporary world model paradigms, this study establishes a new modeling methodology that simultaneously achieves reliability and performance for safety-critical applications.
📝 Abstract
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.