SHF: Small: Learning Circuit Networks from Measurements

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Recent graph-learning techniques exploit both graph topological properties and node-feature (attribute) information to achieve promising results for various important applications such as vertex (data) classification, link prediction (recommendation systems), community detection, drug discovery, partial differential equation (PDE) solvers, and electronic design automation (EDA). On the other hand, graph learning can still be extremely challenging when there exists only partial or no knowledge about the underlying graph topologies. Fortunately, recent research shows that it is possible to learn graph topologies from node-feature (attribute) data so that existing graph-learning algorithms can be applied subsequently. However, even the state-of-the-art graph-topology-learning algorithms do not scale to large data sets due to their high computational complexity, which may prohibit their applications in real-world large-scale graph-learning tasks, such as those adopted for integrated-circuit networks involving billions of components. This project is also likely to spark new research in many other related fields, such as complex system/network modeling, model order reduction, computational biology, precision medicine, and transportation networks. The source code of the developed algorithms will be released on a public website managed by the PI to facilitate technology transfers to the industry, especially to the leading EDA companies. This research project will investigate highly scalable yet sample-efficient spectral methods for learning graph topologies from potentially high-dimensional data samples, such as voltage and current measurements in circuit networks. The proposed approach is based on a novel spectral-graph densification framework to allow for more efficient estimations of attractive Gaussian Markov Random Fields (GMRFs). A unique property of the learned graphs is that the effective-resistance distances on the learned graph will encode the similarities between the original data samples. The success of this research plan will immediately lead to the development of more scalable data-driven, physics-informed EDA algorithms for modeling, simulation, optimization, and verification of integrated circuits (ICs). The accomplished theoretical results will likely advance state of the art in spectral graph theory, dimensionality reduction, scientific computation, data visualization, and machine learning (ML).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.