Related papers: Lean Algebraic Multigrid (LAMG): Fast Graph Laplac…
Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Large language models (LLMs) commonly struggle with specialized or emerging topics which are rarely seen in the training corpus. Graph-based retrieval-augmented generation (GraphRAG) addresses this by structuring domain knowledge as a graph…
Computational modeling of multicellular systems may aid in untangling cellular dynamics and emergent properties of biological cell populations. A key challenge is to balance the level of model detail and the computational efficiency, while…
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…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
Solving large dense linear systems and eigenvalue problems is a core requirement in many areas of scientific computing, but scaling these operations beyond a single GPU remains challenging within modern programming frameworks. While highly…
Linear system solving is one of the main workhorses in applied mathematics. Recently, theoretical computer scientists have contributed sophisticated algorithms for solving linear systems with symmetric diagonally dominant matrices (a class…
Retrieval-augmented generation (RAG) and its graph-based extensions (GraphRAG) are effective paradigms for improving large language model (LLM) reasoning by grounding generation in external knowledge. However, most existing RAG and GraphRAG…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Graph-based computations are crucial in a wide range of applications, where graphs can scale to trillions of edges. To enable efficient training on such large graphs, mini-batch subgraph sampling is commonly used, which allows training…
Multimodal Attributed Graphs (MAGs) are ubiquitous in real-world applications, encompassing extensive knowledge through multimodal attributes attached to nodes (e.g., texts and images) and topological structure representing node…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF)…