Related papers: GMT: A Geometric Multigrid Transformer Solver for …
Geometric problem solving (GPS) requires precise multimodal understanding and rigorous, step-by-step logical reasoning. However, developing capable Multimodal Large Language Models (MLLMs) for GPS is heavily bottlenecked by the scarcity of…
Heterogeneous graph neural networks (HGNNs) are essential for capturing the structure and semantic information in heterogeneous graphs. However, existing GPU-based solutions, such as PyTorch Geometric, suffer from low GPU utilization due to…
We present a parallelized geometric multigrid (GMG) method, based on the cell-based Vanka smoother, for higher order space-time finite element methods (STFEM) to the incompressible Navier--Stokes equations. The STFEM is implemented as a…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
Surrogate modeling is an essential data-driven technique for quantifying relationships between input variables and system responses in manufacturing and engineering systems. Two major challenges limit its effectiveness: (1) large data…
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…
Humans naturally perceive the geometric structure and semantic content of a 3D world as intertwined dimensions, enabling coherent and accurate understanding of complex scenes. However, most prior approaches prioritize training large…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
Recently, 3D Gaussian Splatting (3DGS) has excelled in novel view synthesis (NVS) with its real-time rendering capabilities and superior quality. However, it encounters challenges for high-resolution novel view synthesis (HRNVS) due to the…
Exascale computing delivers the raw power to simulate ever larger and more chemically realistic systems, but realizing this potential requires codes that can efficiently use thousands of processors. Our real-space multigrid (RMG) density…
Efficient hybrid plasmonic-photonic metasurfaces that simultaneously take advantage of the potential of both pure metallic and all-dielectric nanoantennas are identified as an emerging technology in flat optics. Nevertheless,…
Radiance fields represented by 3D Gaussians excel at synthesizing novel views, offering both high training efficiency and fast rendering. However, with sparse input views, the lack of multi-view consistency constraints results in poorly…
3D scene reconstruction is fundamental for spatial intelligence applications such as AR, robotics, and digital twins. Traditional multi-view stereo struggles with sparse viewpoints or low-texture regions, while neural rendering approaches,…
We present a hybrid device platform for creating an electrically reconfigurable metasurface formed by the integration of plasmonic nanostructures with phase-change material germanium antimony telluride (GST). By changing the phase of GST…
Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…
Vision Transformers (ViTs) achieve state-of-the-art performance on challenging vision tasks, but their deployment on edge devices is severely hindered by the computational complexity and global reduction bottleneck imposed by layer…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
We present a hybrid lattice Hamiltonian truncation method that integrates the numerical renormalization group (NRG) with a truncated lattice integrable spectrum. The technique is tailored for generic deformations of integrable lattice…
Simulating fluid-granular flows is crucial for understanding natural disasters, industrial processes, and visually realistic phenomena in computer graphics. These systems are challenging to simulate because of the strong nonlinear coupling…
We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the…