Energy Digest

The article discusses Inductive Correlation Clustering with Graph Neural Networks, which generalizes Correlation Clustering to handle unseen graph instances by leveraging Graph Neural Networks. The proposed framework learns common patterns and node features during training, achieving minimal computational overhead while maintaining competitive results on standard benchmarks. It also serves as an efficient pooling mechanism for graph classification, enhancing the ability of GNNs to capture hierarchical structural information in networks.

A data-driven algorithm using neural networks is proposed to approximate the dominant eigenfunctions of the Koopman operator in nonlinear dynamical systems. The algorithm leverages a power-iteration scheme that directly learns the dominant Koopman modes without requiring explicit construction of a projection matrix. The approach achieves accurate and smooth approximations with theoretical guarantees under increasing sample size and network width.