Related papers: Improved Grid Optimization and Fitting in Least Sq…
Grid supportive (GS) modes integrated within distributed energy resources (DERs) can improve the frequency response. However, synthesis of GS modes for guaranteed performance is challenging. Moreover, a tool is needed to handle…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
In this paper we present a novel geometric filter, a homogeneous moving least squares fitting-based filter (H-MLS filter), for anisotropic mesh filtering. Instead of fitting the noisy data by a moving parametric surface and projecting the…
Spherical centroidal Voronoi tessellations (SCVTs), currently used in numerical weather forecasting models such as the Model for Prediction Across Scales (MPAS), are a type of spherical grid that is highly flexible, allowing the…
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…
An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are…
We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov…
Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with…
Lensless in-line holography is a simple, portable, and cost-effective method of imaging especially for the biomedical microscopy applications. We propose a multiplicative gradient descent optimization based method to obtain multi-depth…
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
Multilevel, multiarea, and hierarchically interconnected electrical power grids confront substantial challenges with the increasing integration of many volatile energy resources. The traditional isolated operation of interconnected power…
Motivated by the recent successes of neural networks that have the ability to fit the data perfectly and generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits…
We consider the problem of fitting a low rank tensor $A\in\mathbb{R}^{{\mathcal I}}$, ${\mathcal I} = \{1,\ldots,n\}^{d}$, to a given set of data points $\{M_i\in\mathbb{R}\mid i\in P\}$, $P\subset{\mathcal I}$. The low rank format under…
Grid clustering algorithms are valued for their efficiency in large-scale data analysis but face persistent limitations: parameter sensitivity, loss of structural detail at coarse resolutions, and misclassifications of edge or bridge cells…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
Limited presence of nodal and line meters in distribution grids hinders their optimal operation and participation in real-time markets. In particular lack of real-time information on the grid topology and infrequently calibrated line…
Totally self-checking (TSC) circuits are synthesised with a grid of computers running a distributed population based stochastic optimisation algorithm. The presented method is the first to automatically synthesise TSC circuits from…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…