Related papers: Tensors in Power System Computation I: Distributed…
Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
Optimal Power Flow (OPF) is an important tool used to coordinate assets in electric power systems to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of…
High-dimensional tensor-valued data have recently gained attention from researchers in economics and finance. We consider the estimation and inference of high-dimensional tensor factor models, where each dimension of the tensor diverges.…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…
A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations. We begin with some examples of CPD applications…
Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
In this paper, we develop an online method that leverages machine learning to obtain feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps on extremely fast timescales (e.g., milliseconds), bypassing…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the…
We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…
The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…
With the rapid development of smart distribution networks (DNs), the integrity and accuracy of grid measurement data are crucial to the safety and stability of the entire system. However, the quality of the user power consumption data…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand.…
Participation factors (PFs) quantify the interaction between system modes and state variables, and they play a crucial role in various applications such as modal analysis, model reduction, and control design. With increasing system…