When do neural ordinary differential equations generalize on complex networks?

arXiv:2602.08980v1 Announce Type: cross
Abstract: Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size or structure than encountered during training. We study neural ODEs ($mathtt{nODE}$s) with vector fields following the Barab’asi-Barzel form, trained on synthetic data from five common dynamical systems on graphs. Using the $mathbb{S}^1$-model to generate graphs with realistic and tunable structure, we find that degree heterogeneity and the type of dynamical system are the primary factors in determining $mathtt{nODE}$s’ ability to generalize across graph sizes and properties. This extends to $mathtt{nODE}$s’ ability to capture fixed points and maintain performance amid missing data. Average clustering plays a secondary role in determining $mathtt{nODE}$ performance. Our findings highlight $mathtt{nODE}$s as a powerful approach to understanding complex systems but underscore challenges emerging from degree heterogeneity and clustering in realistic graphs.