Related papers: Evaluating functions of positive-definite matrices…
We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption…
We propose a new method for computing the $\varphi$-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of $\varphi_{\ell}$-functions of a large matrix to…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
Reliable dynamical properties from molecular dynamics simulations require careful control of thermostatting artifacts. We systematically assess how NVE, deterministic thermostats, velocity-rescale dynamics, and stochastic Langevin-type…
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a…
An estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative…
Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…
A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…
We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…
The complex Langevin method (CLM) offers a potential solution to the sign problem in quantum field theories with complex actions, but can converge to incorrect results even when simulations appear stable. Existing diagnostics monitor drift…
Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a…
This paper focuses on multirate time-domain simulations of power system models. It proposes a matrix pencil-based approach to evaluate the spurious numerical deformation introduced into power system dynamics by a given multirate integration…
We present a supervised machine learning-based method using convolutional neural networks to estimate the covariance matrix of Gaussian quantum states in the presence of thermal noise. Unlike computationally intensive density matrix…
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the…
We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…