Related papers: Accelerating Physics-Based Electromigration Analys…
This paper presents an adaptive sampling algorithm tailored for the optimization of parametrized dynamical systems using projection-based model order reduction. Unlike classical sampling strategies, this framework does not aim for a small…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear…
Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…
Lookahead-based acceleration methods, such as Nesterov's momentum, are widely used in optimization, but they often become unreliable in deep learning training mainly due to stochastic gradient noise and non-convex loss landscapes. In…
Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
An inexact semismooth Newton method has been proposed for solving semi-linear elliptic optimal control problems in this paper. This method incorporates the generalized minimal residual (GMRES) method, a type of Krylov subspace method, to…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
In this paper, we briefly introduce physical foundations of electromigration (EM) and present a few classical EMrelated theories. We discuss physical parameters affecting EM wire lifetime and we introduce some background related to the…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the…
Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
This paper introduces LSEMINK, an effective modified Newton-Krylov algorithm geared toward minimizing the log-sum-exp function for a linear model. Problems of this kind arise commonly, for example, in geometric programming and multinomial…
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…