Neural Operators Can Discover Functional Clusters

Yicen Li, Ruiyang Hong (McMaster)

Monday, February 09, 11:30 (HH403)

Clustering functional data from dynamical systems is challenging as trajectories lie in infinite-dimensional spaces where Euclidean metrics fail. Existing methods often lack theoretical guarantees for converging to the true dynamical structure. We propose a framework for universal clustering of ODE trajectories using Sampling-Based Neural Operators (SNOs). We show that, under sufficient expressivity, SNO-induced decision regions converge to true partitions in the Upper Kuratowski space, a metric well-suited for approximating cluster regions in infinite-dimensional settings. Practically, we instantiate this by discretizing trajectories onto grids, processed by a pre-trained visual encoder and a lightweight clustering head. Experiments on ODE benchmarks demonstrate that our operator-learning approach aligns with theoretical convergence predictions and captures latent structures effectively, outperforming classical baselines.