PhySPRING: Structure-Preserving Reduction of Physics-Informed Digital Twins via Graph Neural Networks

Physics-based digital twins aim to predict the dynamics of real-world objects under interaction, enabling real-to-sim-to-real applications in robotics. Current approaches reconstruct such twins as explicit physical models (such as spring-mass systems) to predict the dynamics, but the resulting models often inherit the resolution of the visual reconstruction rather than being reduced to the physical complexity required to reproduce task-relevant dynamics. This mismatch introduces redundant topology, making repeated forward-dynamics rollouts unnecessarily expensive. To address this challenge, we present PhySPRING, an fully differentiable GNN-based method to reduce complexity in spring--mass digital twins. PhySPRING jointly learns a hierarchy of coarsened graph topologies and their mechanical parameters from observations. At each reduction level, PhySPRING merges nodes with similar learned dynamic responses to optimize the topology, while maintaining every reduced layer as an explicit spring--mass system. On the PhysTwin benchmark, PhySPRING improves dense reconstruction and prediction accuracy over PhysTwin, while reduced models retain stable physical and visual fidelity with up to a 2.30$\times$ speed-up. We further demonstrate the effectiveness of PhySPRING in a Real2Sim robot policy-evaluation pipeline, where the reduced models are substituted zero-shot into ACT and $\pi_0$ evaluations, maintaining comparable manipulation success rates across downsampling levels while improving action-sampling effectiveness. Together, PhySPRING enables efficient and structure-preserving spring--mass reduction without sacrificing fidelity or robotic utility.