Related papers: A universal preconditioner for simulating condense…
Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General…
Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead…
Universal machine learning interatomic potentials (UMLIPs) offer accuracy close to first-principles calculations at a fraction of the cost, showing significant potential for large-scale material simulations. However, the fragmented UMLIPs…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…
Recent years have seen considerable work on compiling sparse tensor algebra expressions. This paper addresses a shortcoming in that work, namely how to generate efficient code (in time and space) that scatters values into a sparse result…
This paper presents a fast method for global search of atomic structures at ab initio level. The structures global optimization (SGO) engine consists of a high-efficiency differential evolution algorithm, accelerated local relaxation…
Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery shelf means that the robot cannot directly access all objects and has limited…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathcal{H}^2$-matrices. We propose several new preconditioners…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that…
The ILU-based preconditioning methods in previous work have their own parameters to improve their performances. Although the parameters may degrade the performance, their determination is left to users. Thus, these previous methods are not…
In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed…
In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order…