Generalization and robustness of neural ODEs for dynamical systems on graphs

Event: IAIFI Summer Workshop 2025, Cambridge, US

Date: 2025/08/13

Abstract

Complex systems from many domains, such as epidemiology, neuroscience, or population dynamics, can be modeled as a graph with node states evolving according to a system of ordinary differential equations (ODEs). Traditionally, these models are hand-crafted by domain experts based on prior knowledge about the system. More recently machine learning methods have been used to forecast complex dynamical systems based on observational data, potentially trading interpretability for predictive performance. Neural ODEs, machine learning models that extract an ODE’s vector field from data, promise to combine the best of both worlds, as they allow incorporating prior knowledge into the architecture while learning details of a given system from empirical time series. While neural ODEs have become an important tool for data-driven modeling, questions of robustness, out-of-distribution generalization, and sample efficiency have only recently moved into the spotlight. Here, we study how incorporating prior knowledge about network dynamical systems into neural ODEs influences generalization to graphs of different sizes and different structural characteristics, as well as their robustness to noise and missing data. We focus on five dynamical systems from different domains and use random hyperbolic graphs as a flexible generative model of graphs with distinct structural characteristics. In this setup, we show empirically that generalization to larger graphs is possible in the case of low degree heterogeneity and exhibits low dependence on the graph’s clustering coefficient. We also show that generalization is possible even for large degree heterogeneity for a limited class of dynamical systems. In addition, we show that generalization performance is mostly robust under noisy training data but degrades quickly when nodes in the graph are unobserved at inference time. While our results on size generalization may pave a route towards efficiency gains by training on smaller graphs, the brittleness to node-missingness serves as a reminder of the limitations of data-driven methods.

Slides

When using these materials, please cite:

@misc{laber2026_neuralODE,
  title = {When do neural ordinary differential equations generalize on complex networks},
  author = {Laber, Moritz and Klein, Brennan and Eliassi-Rad, Tina},
  year = {2026},
  archiveprefix = {arXiv}
  eprint = {2602.08980},
  doi = {10.48550/arXiv.2602.08980}
}