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Graph Neural Networks (GNNs) with equivariant properties have emerged aspowerful tools for modeling complex dynamics of multi-object physical systems.However, their generalization ability is limited by the inadequateconsideration of physical inductive biases: (1) Existing studies overlook thecontinuity of transitions among system states, opting to employ severaldiscrete transformation layers to learn the direct mapping between two adjacentstates; (2) Most models only account for first-order velocity information,despite the fact that many physical systems are governed by second-order motionlaws. To incorporate these inductive biases, we propose the Second-orderEquivariant Graph Neural Ordinary Differential Equation (SEGNO). Specifically,we show how the second-order continuity can be incorporated into GNNs whilemaintaining the equivariant property. Furthermore, we offer theoreticalinsights into SEGNO, highlighting that it can learn a unique trajectory betweenadjacent states, which is crucial for model generalization. Additionally, weprove that the discrepancy between this learned trajectory of SEGNO and thetrue trajectory is bounded. Extensive experiments on complex dynamical systemsincluding molecular dynamics and motion capture demonstrate that our modelyields a significant improvement over the state-of-the-art baselines.

SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases