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Low voltage distribution networks (LVDNs) suffer from limited visibility due to sparse or nonexistent measurement systems, leaving distribution network service providers with incomplete data. Maintenance activities, such as transformer…
We describe two new -- stochastic-geometrical -- methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods,…
We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical…
The increasing integration of distributed energy resources (DERs) calls for new monitoring and operational planning tools to ensure stability and sustainability in distribution grids. One idea is to use existing monitoring tools in…
As Very Large Scale Integration (VLSI) designs continue to scale in size and complexity, layout verification has become a central challenge in modern Electronic Design Automation (EDA) workflows. In practice, congestion can only be…
Reliable electricity supply depends on the seamless operation of high-voltage grid infrastructure spanning both transmission and sub-transmission levels. Beneath this apparent uniformity lies a striking structural diversity, which leaves a…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
Voltage regulation is critical for power grids. However, it has become a much more challenging problem as distributed energy resources (DERs) such as photovoltaic and wind generators are increasingly deployed, causing rapid voltage…
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor…
The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature the model exhibits a disordered solid…
The discovery of new catalysts is one of the significant topics of computational chemistry as it has the potential to accelerate the adoption of renewable energy sources. Recently developed deep learning approaches such as graph neural…
In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks…
The increasing penetration of variable renewable energy (VRE) has brought significant challenges for power systems planning and operation. These highly variable sources are typically distributed in the grid; therefore, a detailed…
Volumetric shape representations have become ubiquitous in multi-view reconstruction tasks. They often build on regular voxel grids as discrete representations of 3D shape functions, such as SDF or radiance fields, either as the full shape…
Accurate voltage estimation in distribution networks is critical for real-time monitoring and increasing the reliability of the grid. As DER penetration and distribution level voltage variability increase, robust distribution system state…
The application of graph neural networks (GNNs) to the domain of electrical power grids has high potential impact on smart grid monitoring. Even though there is a natural correspondence of power flow to message-passing in GNNs, their…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
Voronoi diagrams are highly compact representations that are used in various Graphics applications. In this work, we show how to embed a differentiable version of it -- via a novel deep architecture -- into a generative deep network. By…
Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics…