Related papers: Improved Grid Optimization and Fitting in Least Sq…
This paper proposes a new strategy for optimal grid frequency regulation (FR) in an interconnected power system where regional ac grids and an offshore wind farm are linked via a multi-terminal high voltage direct-current (MTDC) network. In…
We introduce a low-rank framework for adaptive isogeometric analysis with truncated hierarchical B-splines (THB-splines) that targets the main bottleneck of local refinement: memory- and time-intensive matrix assembly once the global…
We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is not always possible to sample functions at optimal nodes…
Hyperspectral images~(HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multi-scale low-rank tensor regularized $\ell_{2,p}$ (MLTL2p) approach for HSI…
Recently, the finite-rate-of-innovation (FRI) based continuous domain regularization is emerging as an alternative to the conventional on-the-grid sparse regularization for the compressed sensing (CS) due to its ability to alleviate the…
In this work we present an attractive least-squares fitting procedure to obtain a quartic force field by using energy, gradient and Hessian data arising from electronic wave function calculations on a suitably chosen grid of points. We use…
We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition. Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications. We propose an algorithm…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…
In this article, we present an interpolative separable density fitting (ISDF) based algorithm to calculate exact exchange in periodic mean field calculations. In the past, decomposing the two-electron integrals into tensor hypercontraction…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
This paper proposes a transient stability-driven planning framework for the optimal sizing problem of resilient AC/DC hybrid microgrids (HMGs) under different types of contingencies, capturing frequency and voltage stability requirements as…
This paper introduces the stochastic Fej\'{e}r-monotone hybrid steepest descent method (S-FM-HSDM) to solve affinely constrained and composite convex minimization tasks. The minimization task is not known exactly; noise contaminates the…
Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a $d$-dimensional tensor product space, the number of grid points is $N = \mathcal O(h^{-1} |\log h|^{d-1})$, where $h$ is a mesh parameter. The…
Optical microrobots actuated by optical tweezers (OT) offer great potential for biomedical applications such as cell manipulation and microscale assembly. These tasks demand accurate three-dimensional perception to ensure precise control in…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
This work develops a framework to create meshes with user-specified homology from potentially dirty geometry by coupling background grids, persistent homology, and a generalization of volume fractions. For a mesh with fixed grid size, the…
We investigate the efficient combination of the canonical polyadic decomposition (CPD) and tensor hyper-contraction (THC) approaches. We first present a novel low-cost CPD solver which leverages a precomputed THC factorization of an…
The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…