Related papers: A reduced basis warm-start iterative solver for th…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
Traditional recommendation systems rely on past usage data in order to generate new recommendations. Those approaches fail to generate sensible recommendations for new users and items into the system due to missing information about their…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
Reduced Basis Methods (RBMs) are frequently proposed to approximate parametric problem solutions. They can be used to calculate solutions for a large number of parameter values (e.g. for parameter fitting) as well as to approximate a…
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…