EvolveODE: Emulating Underlying Dynamics through Sorting and Coupling

Observational-level data arises from processes beyond the scope of direct observation. These processes naturally couple across the scales they natively occupy. In real-world settings, they may include global weather subsystems and time-delayed traffic flows, among other such systems. Through self-attention, Graph Neural Networks (GNNs) offer a natural way to untangle these confounding factors, namely by leveraging self-organization to sort variables that strongly interact with one another, forming a sub-process. We propose EvolveODE, a multiscale GNN that solves attraction-repulsion equations to identify groupings, thereby learning the coupling between the physical processes underlying observation-level phenomena. EvolveODE then emulates these relationships with a dynamical system. We show that EvolveODE outperforms the current state-of-the-art baselines across various tasks and settings. Code is available at https://anonymous.4open.science/r/EvolveODE/.