Graph-Operator World Models for Morphology-Parameter Generalization in Continuous Control

Graph-Operator World Models (GraphOp-WM) are a structured approach to learning world models that generalize across varying morphology parameters in continuous control tasks. The model represents robot bodies and their kinematic relationships as an attributed graph, decomposing each transition into a morphology‑independent local dynamics basis and a morphology‑conditioned structured operator. This operator blends node‑local modulation, kinematic‑tree coupling, and a low‑rank global correction, while architectural design choices encourage the operator to capture static morphology dependence. The framework supports reward, value, and TD‑MPC‑style planning through graph‑level readout and edge‑wise action representations, and is evaluated on controlled MuJoCo parameter splits involving interpolation, extrapolation, and held‑out compositions of link geometry, mass, damping, and actuation in Hopper, Walker2d, and HalfCheetah.