Learning Networked Dynamical Systems via Neural ODE-based Graph Structure Inference

Inferring the latent interaction graph from multivariate time series is fundamental to understanding complex dynamical systems in neuroscience, biology, and physics. Despite recent progress in neural relational inference, most methods rely on discrete-time modeling, which degrades under sparse and irregular observations and tends to entangle multi-hop dependencies into spurious direct edges. We show that a continuous-time formulation naturally decouples inference from any fixed observation schedule, allowing gradient signals to be integrated continuously between observations for both dynamics and structure learning. We propose NOGI (Neural ODE-based Graph Inference), a framework that couples a deterministic graph learner with an MPNN-based Neural ODE. The two modules are trained end-to-end via the adjoint method with $\mathcal{O}(1)$ memory cost. Across four simulated dynamical systems at two scales, NOGI achieves the best structure recovery in 30 out of 32 evaluated cases with highly competitive forecasting performance, remaining robust under observation degradation. On the realistic Netsim fMRI benchmark, it attains an average AUPRC of 0.90 (AUROC 0.96). These results suggest that explicitly decoupling relational interactions from self-dynamics within a continuous-time vector field provides a powerful mechanism for graph structure learning under realistic observation conditions.