Neural Koopman forecasting for critical transitions in infrastructure networks

We develop a data-driven framework for long-term forecasting of stochastic dynamics on evolving networked infrastructure systems using neural approximations of Koopman operators. In real-world nonlinear systems, the exact Koopman operator is infinite-dimensional and generally unavailable in closed form, necessitating learned finite-dimensional surrogates. Focusing on applications such as traffic flow and power grid oscillations, we model the underlying dynamics as random graph-driven nonlinear processes and introduce a graph-informed neural architecture that learns approximate Koopman eigenfunctions to capture system evolution over time. Our key contribution is the joint treatment of stochastic network evolution, Koopman operator learning, and phase-transition-induced breakdowns in forecasting. We identify critical regimes—arising from graph connectivity shifts or load-induced bifurcations—where the effective forecasting horizon collapses due to spectral degeneracy in the learned Koopman operator. We establish sufficient conditions under which this collapse occurs and propose regularization techniques to mitigate representational breakdown. Numerical experiments on traffic and power networks validate the proposed method and confirm the emergence of critical behavior. These results not only highlight the challenges of forecasting near structural transitions, but also suggest that spectral collapse may serve as a diagnostic signal for detecting phase transitions in dynamic networks. Our contributions unify spectral operator theory, random dynamical systems, and neural forecasting into a control-theoretic framework for real-time intelligent infrastructure. To our knowledge, this is the first work to jointly study Koopman operator learning, stochastic network evolution, and forecasting collapse induced by graph-theoretic phase transitions.