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Visual Simultaneous Localization and Mapping (VSLAM) research faces significant challenges due to fragmented toolchains, complex system configurations, and inconsistent evaluation methodologies. To address these issues, we present…

Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian…

The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques…

In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…

Large-scale linear complementarity problems (LCPs) are repeatedly solved in interactive rigid-body simulations. The projected Gauss-Seidel method is often employed for LCPs, since it has advantages in computation time, numerical robustness,…

The integration of visual inputs with large language models (LLMs) has led to remarkable advancements in multi-modal capabilities, giving rise to visual large language models (VLLMs). However, effectively harnessing VLLMs for intricate…

In federated learning (FL), model training performance is strongly impacted by data heterogeneity across clients. Client-drift compensation methods have recently emerged as a solution to this issue, introducing correction terms into local…

This paper introduces the Scaled Coordinate Transformation Boundary Element Method (SCTBEM), a novel boundary-type method for solving 3D potential problems. To address the challenges of applying the Boundary Element Method (BEM) to complex…

This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of {\em straggling} processors. To mitigate the effect of the stragglers, it has been previously…

In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…

We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection…

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on…

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing…

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss…

Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer…

Vector quantization (VQ) is a key technique in high-resolution and high-fidelity image synthesis, which aims to learn a codebook to encode an image with a sequence of discrete codes and then generate an image in an auto-regression manner.…

We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

General matrix-vector multiplication (GeMV) remains a critical latency bottleneck in large language model (LLM) inference, even with quantized low-bit models. Processing-Using-DRAM (PUD), an analog in-DRAM computing technique, has the…