Graph Fourier Neural ODEs: Modeling Spatial-temporal Multi-scales in Molecular Dynamics
Abstract: Accurately predicting long-horizon molecular dynamics (MD) trajectories remains a significant challenge, as existing deep learning methods often struggle to retain fidelity over extended simulations. We hypothesize that one key factor limiting accuracy is the difficulty of capturing interactions that span distinct spatial and temporal scales-ranging from high-frequency local vibrations to low-frequency global conformational changes. To address these limitations, we propose Graph Fourier Neural ODEs (GF-NODE), integrating a graph Fourier transform for spatial frequency decomposition with a Neural ODE framework for continuous-time evolution. Specifically, GF-NODE first decomposes molecular configurations into multiple spatial frequency modes using the graph Laplacian, then evolves the frequency components in time via a learnable Neural ODE module that captures both local and global dynamics, and finally reconstructs the updated molecular geometry through an inverse graph Fourier transform. By explicitly modeling high- and low-frequency phenomena in this unified pipeline, GF-NODE more effectively captures long-range correlations and local fluctuations alike. Experimental results on challenging MD benchmarks, including MD17 and alanine dipeptide, demonstrate that GF-NODE achieves state-of-the-art accuracy while preserving essential geometrical features over extended simulations. These findings highlight the promise of bridging spectral decomposition with continuous-time modeling to improve the robustness and predictive power of MD simulations. Our implementation is publicly available at https://anonymous.4open.science/r/GF-NODE-code-B289/
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Kamyar_Azizzadenesheli1
Submission Number: 4477
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