Related papers: An accelerated linear method for optimizing non-li…
A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…
This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…
A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially…
We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…