Where Structure Enters a World Model: From Predictive Fit to Physical Rollout

Predictive world models learn to forecast observations, but accurate short-term predictions do not necessarily produce physically coherent behavior over longer horizons. We investigate how incorporating physical structure can strengthen world models while retaining their underlying predictive objectives. Across token-based models of planetary motion and JEPA-style visual models of mechanical systems, we study conserved-quantity supervision, symmetry-aware representations, temporal consistency, and learned structured dynamics. In planetary motion, angular-momentum supervision improves autonomous next-token forecasting, while the benefits of temporal regularization depend on the accompanying physical objective and representation. In visual models, generating rollouts through supervised energy-based dynamics heads produces more faithful trajectories and phase-space evolution. Together, these findings highlight the importance of how physical structure participates in prediction: improvements in an auxiliary physical readout or a local acceleration estimate do not automatically translate into more reliable long-horizon behavior. Evaluations across initial conditions and physical parameter shifts further reveal where these benefits persist and where generalization remains limited. Our study supports physical structure as a practical means of improving predictive world models and provides a unified framework for understanding its effects on representations, learned transitions, and autonomous rollouts. The central lesson is that effective physical inductive biases should help models both represent physical regularities and use them to generate future states.