Related papers: GL-Coarsener: A Graph representation learning fram…
The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined…
Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…
While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…
Graph Neural Networks (GNNs) are powerful techniques in representation learning for graphs and have been increasingly deployed in a multitude of different applications that involve node- and graph-wise tasks. Most existing studies solve…
Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
We propose an adaptive graph coarsening method to jointly learn graph neural network (GNN) parameters and merge nodes via K-means clustering during training. As real-world graphs grow larger, processing them directly becomes increasingly…
We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the…
Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…
In recent years, numerous graph generative models (GGMs) have been proposed. However, evaluating these models remains a considerable challenge, primarily due to the difficulty in extracting meaningful graph features that accurately…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion…
Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…