Related papers: Supernodal Analysis Revisited
Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling.…
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
We propose split-brain autoencoders, a straightforward modification of the traditional autoencoder architecture, for unsupervised representation learning. The method adds a split to the network, resulting in two disjoint sub-networks. Each…
Independent Component Analysis (ICA) is a statistical tool that decomposes an observed random vector into components that are as statistically independent as possible. ICA over finite fields is a special case of ICA, in which both the…
Graph Neural Networks (GNNs) have recently emerged as a robust framework for graph-structured data. They have been applied to many problems such as knowledge graph analysis, social networks recommendation, and even Covid19 detection and…
We consider algorithmic problems in the setting in which the input data has been partitioned arbitrarily on many servers. The goal is to compute a function of all the data, and the bottleneck is the communication used by the algorithm. We…
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…
Two approaches for graph based semi-supervised learning are proposed. The firstapproach is based on iteration of an affine map. A key element of the affine map iteration is sparsematrix-vector multiplication, which has several very…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a novel autoencoder architecture capable of learning a joint representation of both local…
Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…
The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where…
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…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Circuit cutting is a promising technique that leverages both quantum and classical computational resources, enabling the practical execution of large quantum circuits on noisy intermediate-scale quantum (NISQ) hardware. Recent approaches…
With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to…
We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging…