Related papers: Integrating Additive Multigrid with Multiprecondit…
Graph Neural Networks (GNNs) have achieved promising performance in semi-supervised node classification in recent years. However, the problem of insufficient supervision, together with representation collapse, largely limits the performance…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…
We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers…
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…
In this paper we propose a multigrid optimization algorithm (MG/OPT) for the numerical solution of a class of quasilinear variational inequalities of the second kind. This approach is enabled by the fact that the solution of the variational…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
In this paper, we develop an EXCMG method to solve the three-dimensional Poisson equation on rectangular domains by using the compact finite difference (FD) method with unequal meshsizes in different coordinate directions. The resulting…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems.…
Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice and plays an important role in the generalization of modern machine learning. However, prior research has revealed instances where the…
Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…
In this paper, we propose a modified nonlinear conjugate gradient (NCG) method for functions with a non-Lipschitz continuous gradient. First, we present a new formula for the conjugate coefficient \beta_k in NCG, conducting a search…
This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by the full bootstrap algebraic multigrid (BAMG) setup algorithm that includes an…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
Multivariate time series prediction is widely used in daily life, which poses significant challenges due to the complex correlations that exist at multi-grained levels. Unfortunately, the majority of current time series prediction models…
Coarse grid projection (CGP) multigrid techniques are applicable to sets of equations that include at least one decoupled linear elliptic equation. In CGP, the linear elliptic equation is solved on a coarsened grid compared to the other…