Spectral-guided Physical Dynamics Distillation

The problem of physical dynamics, which involves predicting the 3D trajectories of particles, is a fundamental task with wide-ranging applications across science and engineering. However, accurately forecasting long-horizon trajectories from initial states remains challenging, due to complex particle interactions and entangled multi-scale dynamics involving both low-and high-frequency components. To address this, we propose a novel knowledge-distillation-based framework, SGDD (Spectral-Guided Dynamics Distillation), which integrates a spectral-guided enhancement to adaptively prioritize key frequency components within a unified spatio-temporal representation. Through knowledge distillation, SGDD leverages future trajectories as privileged information during training, guiding a teacher encoder to generate comprehensive dynamics representations while a student encoder approximates them using only the initial state. This enables the student to generate effective dynamics representations at inference, even without privileged information, thereby enabling accurate long-horizon trajectory prediction. Experimental results on molecule, protein, and human motion datasets demonstrate that our method achieves more accurate and stable long-term predictions than previous physical dynamics models, successfully capturing the complex spatio-temporal structures of real-world systems. Recent efforts extend beyond spatial equivariance to explicitly address temporal evolution. ESTAG (Wu et al., 2023a) employed an Equivariant DFT together with spatio-temporal modules to capture periodic and non-Markovian behaviors. EGNO (Xu et al., 2024) formulated an Equivariant Graph Neural Operator that directly models trajectories via Fourier-based temporal convolutions. GF-NODE (Sun et al., 2024) integrated Graph Fourier decomposition with Neural ODEs to couple local high-frequency and global low-frequency dynamics.