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Several methods exist today to accelerate Machine Learning(ML) or Deep-Learning(DL) model performance for training and inference. However, modern techniques that rely on various graph and operator parallelism methodologies rely on search…
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional…
Power flow in a low voltage direct current grid (LVDC) is a non-linear problem just as its counterpart ac. This paper demonstrates that, unlike in ac grids, convergence and uniqueness of the solution can be guaranteed in this type of grids.…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes…
We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…
A new method for solving Laplacian linear systems proposed by Kelner et al. involves the random sampling and update of fundamental cycles in a graph. Kelner et al. proved asymptotic bounds on the complexity of this method but did not report…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central…
Addressing challenges in urban water infrastructure systems including aging infrastructure, supply uncertainty, extreme events, and security threats, depend highly on water distribution networks modeling emphasizing the importance of…
This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum $s$-$t$ flow and maximum concurrent…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path…
The graph Laplacian, a typical representation of a network, is an important matrix that can tell us much about the network structure. In particular its eigenpairs (eigenvalues and eigenvectors) incubate precious topological information…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…
Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic…
The effectiveness of contrastive learning methods has been widely recognized in the field of graph learning, especially in contexts where graph data often lack labels or are difficult to label. However, the application of these methods to…