Reducing operator complexity in Algebraic Multigrid with Machine Learning Approaches
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on spectrally equivalent coarse-grid operators, we have developed novel ML algorithms that utilize neural networks (NNs) combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall AMG convergence for solving parametric partial differential equation (PDE) problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and compare with existing methods for computing non-Galerkin coarse-grid operators.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most comm…
reinforcement-learningReinforcement LearningReinforcement Learning (RL)Algebraic multigrid support vector machines
The support vector machine is a flexible optimization-based technique widely used for classification problems. In practice, its training part becomes computationally expensive on large-scale data sets because of such rea…
General ClassificationDiffGCN: Graph Convolutional Networks via Differential Operators and Algebraic Multigrid Pooling
Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from…
Acceleration of an algebraic multigrid pressure solver using graph neural networks
Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularitie…
Graph Neural NetworkM2NO: Multiresolution Operator Learning with Multiwavelet-based Algebraic Multigrid Method
Solving partial differential equations (PDEs) effectively necessitates a multi-scale approach, particularly critical in high-dimensional scenarios characterized by increasing grid points or resolution. Traditional method…
Operator learningSuper-Resolution