Neural Transfer Operators for Predicting Ergodic Behavior in Evolving Networks

TMLR Paper5193 Authors

Abstract: We propose a neural operator learning framework for approximating the Perron–Frobenius transfer operator associated with stochastic dynamics on evolving networks. Our objective is to predict long-term ergodic behavior—such as convergence to equilibrium, oscillatory regimes, or systemic collapse—based on observed trajectories and time-varying graph structures. We develop a rigorous theoretical foundation for the convergence of neural approximations to the true transfer operator, under appropriate regularity, mixing, and sample complexity conditions. Moreover, we demonstrate that near critical transitions—such as percolation thresholds or synchronization breakdowns—the spectral properties of the learned operator exhibit universal signatures, including spectral gap closure and eigenvalue bifurcation. These phenomena provide early indicators of ergodicity breaking and metastability. We illustrate the framework on models of traffic flow and power distribution in smart cities, showing that the learned spectral geometry enables robust forecasting of resilience and failure modes. This work bridges spectral theory, random dynamical systems, and machine learning, and provides a foundational step toward AI-enabled predictive infrastructure analytics.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=YUrdks1Z53&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

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Assigned Action Editor: ~Kenta_Oono1

Submission Number: 5193