Related papers: Efficient FPGA Implementation of Conjugate Gradien…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
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…
The classical line search for learning rate (LR) tuning in the stochastic gradient descent (SGD) algorithm can tame the convergence slowdown due to data-sampling noise. In a federated setting, wherein the client heterogeneity introduces a…
Gradient-based distributed learning in Parameter Server (PS) computing architectures is subject to random delays due to straggling worker nodes, as well as to possible communication bottlenecks between PS and workers. Solutions have been…
This paper proposes a generalization of the conjugate gradient (CG) method used to solve the equation $Ax=b$ for a symmetric positive definite matrix $A$ of large size $n$. The generalization consists of permitting the scalar control…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
In this study, we propose a novel parallel processing method for point cloud ground segmentation, aimed at the technology evolution from mechanical to solid-state Lidar (SSL). We first benchmark point-based, grid-based, and range…
FPGAs offer high performance, low latency, and energy efficiency for accelerated computing, yet adoption in scientific and edge settings is limited by the specialized hardware expertise required. High-level synthesis (HLS) boosts…
3D Gaussian Splatting (3DGS) based Simultaneous Localization and Mapping (SLAM) systems can largely benefit from 3DGS's state-of-the-art rendering efficiency and accuracy, but have not yet been adopted in resource-constrained edge devices…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
Balancing (equalization) of latency in parallel paths in the pipelined data processing system is an important problem. Without that the data from different paths arrive at the processing blocks in different clock cycles, and incorrect…
We investigate structured grids aligned to the contours of a two-dimensional flux-function with an X-point (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the flux-function vanishes…
The Animation-based Generative Codec (AGC) is an emerging paradigm for talking-face video compression. However, deploying its intricate decoder on resource and power-constrained edge devices presents challenges due to numerous parameters,…
Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…
While distributed training significantly speeds up the training process of the deep neural network (DNN), the utilization of the cluster is relatively low due to the time-consuming data synchronizing between workers. To alleviate this…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…