Related papers: Solving Convolution-type Integral Equations using …

At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…

Machine learning is evolving towards high-order models that necessitate pre-training on extensive datasets, a process associated with significant overheads. Traditional models, despite having pre-trained weights, are becoming obsolete due…

This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…

The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the…

This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight…

Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm, has been proposed. The main computational cost of the AIRGA…

Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…

In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trained to learn operators and solve differential equations…

Shifted Laplacian multigrid preconditioner has become a tool du jour for solving highly indefinite Helmholtz equations. The idea is to add a complex damping to the original Helmholtz operator and then apply a multigrid processing to the…

We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation…

The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…

When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…

Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…