Related papers: GMT: A Geometric Multigrid Transformer Solver for …
The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation…
Geometric graph neural networks (GNNs) excel at capturing molecular geometry, yet their locality-biased message passing hampers the modeling of long-range interactions. Current solutions have fundamental limitations: extending cutoff radii…
We propose a material-aware optimization framework for high-fidelity mesh reconstruction from multi-view images based on 3D Gaussian Splatting, referred to as GS-2M. Previous works handle these tasks separately and struggle to reconstruct…
This paper introduces a geometric multigrid preconditioner for the Shifted Boundary Method (SBM) designed to solve PDEs on complex geometries. While SBM simplifies mesh generation by using a non-conforming background grid, it often results…
The versatile physical properties of heterogeneous materials are intimately related to their complex microstructures, which can be statistically characterized and modelled using various spatial correlation functions containing key…
Despite decades of research, creating accurate, robust, and efficient lattice Boltzmann methods (LBM) on non-uniform grids with seamless GPU acceleration remains challenging. This work introduces a novel strategy to address this challenge…
Novel view synthesis (NVS) aims to generate images at arbitrary viewpoints using multi-view images, and recent insights from neural radiance fields (NeRF) have contributed to remarkable improvements. Recently, studies on generalizable NeRF…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
We investigate how to generate multimodal image outputs, such as RGB, depth, and surface normals, with a single generative model. The challenge is to produce outputs that are realistic, and also consistent with each other. Our solution…
Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…
GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corresponding Green's…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…
We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…
Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are currently stagnate. This situation has created the well-known bottleneck for…
Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably…
Recently, 3D Gaussian Splatting and its derivatives have achieved significant breakthroughs in large-scale scene reconstruction. However, how to efficiently and stably achieve high-quality geometric fidelity remains a core challenge. To…