Related papers: Localized Sparsifying Preconditioner for Periodic …
We comment on article by Yi Zhang , Hanna Terletska, Ka-Ming Tam, Yang Wang, Markus Eisenbach, Liviu Chioncel, and Mark Jarrell [Phys. Rev. B {\bf 100}, 054205 (2019)]\cite{Zhang} in which to study substitution disordered systems, they…
Conformal Prediction is a robust framework that ensures reliable coverage across machine learning tasks. Although recent studies have applied conformal prediction to graph neural networks, they have largely emphasized post-hoc prediction…
In this paper we extend the deterministic sublinear FFT algorithm in Plonka et al. (2018) for fast reconstruction of $M$-sparse vectors ${\mathbf x}$ of length $N= 2^J$, where we assume that all components of the discrete Fourier transform…
This paper proposes localized subspace iteration (LSI) methods to construct generalized finite element basis functions for elliptic problems with multiscale coefficients. The key components of the proposed method consist of the localization…
Although the classification of crystalline materials can be generally handled by momentum-space-based approaches, topological classification of aperiodic materials remains an outstanding challenge, as the absence of translational symmetry…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…
When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of…
Sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented. An approximate predictor is a mapping which approximates the exact values of the stabilizing input for…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
First-principles density functional theory (DFT) codes which employ a localized basis offer advantages over those which use plane-wave bases, such as better scaling with system size and better suitability to low-dimensional systems. The…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
This paper introduces SparseTSF, a novel, extremely lightweight model for Long-term Time Series Forecasting (LTSF), designed to address the challenges of modeling complex temporal dependencies over extended horizons with minimal…
This paper introduces a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least-squares Petrov-Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system $Ax=b$ with $A$ irregular sparse, i.e., with $A$ having $s$ relatively dense columns, SPAI may be…
Fully finetuning foundation language models (LMs) with billions of parameters is often impractical due to high computational costs, memory requirements, and the risk of overfitting. Although methods like low-rank adapters help address these…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…