Related papers: Enhanced Relaxed Physical Factorization preconditi…
The increasing size of transformer-based models in NLP makes the question of compressing them important. In this work, we present a comprehensive analysis of factorization based model compression techniques. Specifically, we focus on…
Hamiltonian simulation using product formulas is arguably the most straightforward and practical approach for algorithmic simulation of a quantum system's dynamics on a quantum computer. Here we present corrected product formulas (CPFs), a…
We consider a modification of the so-called phase-field crystal (PFC) equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
The nuclear fuel loading pattern optimization problem belongs to the class of large-scale combinatorial optimization. It is also characterized by multiple objectives and constraints, which makes it impossible to solve explicitly. Stochastic…
We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix…
We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
A preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with parameter-dependent matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial…
Representation Fine-tuning (ReFT), a recently proposed Parameter-Efficient Fine-Tuning (PEFT) method, has attracted widespread attention for significantly improving parameter efficiency by editing representation space alone. In this work,…
Regularized empirical risk minimization (rERM) has become important in data-intensive fields such as genomics and advertising, with stochastic gradient methods typically used to solve the largest problems. However, ill-conditioned…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address…
The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…
Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…