What Moves Together: Compositional Motion Modes for Physical Dynamics Prediction

Physical dynamics prediction aims to forecast the trajectories of interacting components across diverse physical systems, from atoms in molecules to joints in human motion. The dynamics of such systems combine distinct but interacting kinds of motion: system-wide translation and rotation, system-wide deformation, and neighborhood-level motion. However, most existing approaches predict the resulting trajectory without explicitly separating these kinds of motion, leaving their individual contributions and interactions entangled. We introduce Compositional Mode Dynamics (CMD), a framework that represents physical motion with a compositional mode dictionary and models how its coefficients evolve and interact. The dictionary collects the spatial patterns of modes, grouped into three complementary families: rigid, collective, and local. Each mode follows its own linear dynamics, while structured coupling allows interactions within and across mode families without changing the underlying modal dynamics. This formulation yields an explicit and interpretable decomposition of predicted trajectories into physically meaningful motion components. Experiments on molecular dynamics and human motion datasets show that CMD achieves competitive prediction performance, while ablations and analyses validate the roles of the mode families and their coupled coefficient dynamics.