Yeomoon Kim | Searcharxiv

arXiv2026

Paths to synchronization in the Kuramoto model with inertia

Synchronization is ubiquitous across natural and synthetic systems, yet most prior studies focus on the inertia-free Kuramoto model and do so at the macroscopic level. In this study, we instead investigate the inertial Kuramoto model and analyze the kinetics of individual synchronized clusters that emerge in the underdamped dynamics, driven by the interactions among multiple synchronized clusters with different frequencies. Specifically, we explore two forms of intrinsic frequency distribution -- unimodal Gaussian and multimodal uniform -- and show that they give rise to qualitatively different synchronized clusters: a hierarchical organization for the Gaussian distribution and a homogeneous organization for the uniform distribution. This contrast leads to qualitatively different behaviors of the order parameter: for the Gaussian distribution, it increases smoothly with increasing coupling strength, while for the uniform distribution, it grows through a series of discrete jumps that trace out the size of the Devil's staircase (DS). By resolving the kinetics at the cluster level, we further find that the route to synchronization also depends on the distribution type: with a Gaussian distribution, a single dominant cluster forms and gradually entrains the remaining oscillators, whereas with a uniform distribution, synchronization proceeds via successive cluster mergers initiated from peripheral seeds associated with the high-frequency periphery. Taken together, these findings provide a new perspective on collective synchronization dynamics in inertial complex systems.

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arXiv2025

MPA-DNN: Projection-Aware Unsupervised Learning for Multi-period DC-OPF

Ensuring both feasibility and efficiency in optimal power flow (OPF) operations has become increasingly important in modern power systems with high penetrations of renewable energy and energy storage. While deep neural networks (DNNs) have emerged as promising fast surrogates for OPF solvers, they often fail to satisfy critical operational constraints, especially those involving inter-temporal coupling, such as generator ramping limits and energy storage operations. To deal with these issues, we propose a Multi-Period Projection-Aware Deep Neural Network (MPA-DNN) that incorporates a projection layer for multi-period dispatch into the network. By doing so, our model enforces physical feasibility through the projection, enabling end-to-end learning of constraint-compliant dispatch trajectories without relying on labeled data. Experimental results demonstrate that the proposed method achieves near-optimal performance while strictly satisfying all constraints in varying load conditions.

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