Related papers: Enhancing data locality of the conjugate gradient …
This paper presents distributed adaptive algorithms based on the conjugate gradient (CG) method for distributed networks. Both incremental and diffusion adaptive solutions are all considered. The distributed conventional (CG) and modified…
To find deterministic solutions to the transient $S_N$ neutron transport equation, iterative schemes are typically used to treat the scattering (and fission) source terms. We explore the one-cell inversion iteration scheme to do this on the…
We revise the problem of extracting one independent component from an instantaneous linear mixture of signals. The mixing matrix is parameterized by two vectors, one column of the mixing matrix and one row of the de-mixing matrix. The…
Minimizing a convex function over the spectrahedron, i.e., the set of all positive semidefinite matrices with unit trace, is an important optimization task with many applications in optimization, machine learning, and signal processing. It…
A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…
Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A…
The performance of eigenvalue problem solvers (eigensolvers) depends on various factors such as preconditioning and eigenvalue distribution. Developing stable and rapidly converging vectorwise eigensolvers is a crucial step in improving the…
The increasing prevalence of large-scale graphs poses a significant challenge for graph neural network training, attributed to their substantial computational requirements. In response, graph condensation (GC) emerges as a promising…
Contingency analysis (CA) plays a critical role to guarantee operation security in the modern power systems. With the high penetration of renewable energy, a real-time and comprehensive N-1 CA is needed as a power system analysis tool to…
We study algorithmic approaches for recovering from the failure of several compute nodes in the parallel preconditioned conjugate gradient (PCG) solver on large-scale parallel computers. In particular, we analyze and extend an exact state…
Projection-free conditional gradient (CG) methods are the algorithms of choice for constrained optimization setups in which projections are often computationally prohibitive but linear optimization over the constraint set remains…
In this paper, we propose a 'full-stack' solution to designing high capacity and low latency on-chip cache hierarchies by starting at the circuit level of the hardware design stack. First, we propose a novel Gain Cell (GC) design using…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…