The paper proposes three new, general, hierarchical frameworks for community detection in complex networks. These methods leverage node similarity, graph representation learning, and hierarchical clustering to handle the challenge. The approach successfully integrates linkage-based clustering, proximity matrices, and deep learning representations. The best pipelines developed are competitive with state-of-the-art algorithms like Leiden and Louvain while maintaining hierarchical output. Although effective, the framework has a time complexity limitation on large graphs.
A novel kernel-based framework is introduced to learn differential equations and their corresponding solution operators efficiently. This method is data-efficient, requiring fewer observed states and less data per state. The training procedure utilizes efficient Gauss-Newton-type optimization algorithms to enhance accuracy and speed. The framework provides theoretical guarantees through quantitative worst-case error bounds for the learned equation and solution operators. Benchmarks show significant improvements in computational complexity and accuracy over state-of-the-art methods.